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{{task|Prime numbers}}
Humble numbers are positive integers which have no prime factors > '''7'''.
Humble numbers are also called ''7-smooth numbers'', and sometimes called ''highly composite'',
although this conflicts with another meaning of ''highly composite numbers''.
Another way to express the above is:
humble = 2i × 3j × 5k × 7m
where <big> i, j, k, m <big>≥</big> 0 </big>
;Task: :* show the first '''50''' humble numbers (in a horizontal list) :* show the number of humble numbers that have '''x''' decimal digits for all '''x's''' up to '''n''' (inclusive). :* show (as many as feasible or reasonable for above) on separate lines :* show all output here on this page
;Related tasks: :* [[Hamming numbers]]
;References: :* [https://en.wikipedia.org/wiki/Smooth_number#Definition smooth numbers, see the 2nd paragraph] :* [http://oeis.org/A002473 OEIS A002473 humble numbers] :* [http://www.informatik.uni-ulm.de/acm/Locals/1996/number.sol University of Ulm, The first 5842 terms of humble numbers]
C++
{{trans|Kotlin}}
#include <iomanip> #include <iostream> #include <map> #include <sstream> bool isHumble(int i) { if (i <= 1) return true; if (i % 2 == 0) return isHumble(i / 2); if (i % 3 == 0) return isHumble(i / 3); if (i % 5 == 0) return isHumble(i / 5); if (i % 7 == 0) return isHumble(i / 7); return false; } auto toString(int n) { std::stringstream ss; ss << n; return ss.str(); } int main() { auto limit = SHRT_MAX; std::map<int, int> humble; auto count = 0; auto num = 1; while (count < limit) { if (isHumble(num)) { auto str = toString(num); auto len = str.length(); auto it = humble.find(len); if (it != humble.end()) { it->second++; } else { humble[len] = 1; } if (count < 50) std::cout << num << ' '; count++; } num++; } std::cout << "\n\n"; std::cout << "Of the first " << count << " humble numbers:\n"; num = 1; while (num < humble.size() - 1) { auto it = humble.find(num); if (it != humble.end()) { auto c = *it; std::cout << std::setw(5) << c.second << " have " << std::setw(2) << num << " digits\n"; num++; } else { break; } } return 0; }
{{out}}
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
Of the first 32767 humble numbers:
9 have 1 digits
36 have 2 digits
95 have 3 digits
197 have 4 digits
356 have 5 digits
579 have 6 digits
882 have 7 digits
1272 have 8 digits
1767 have 9 digits
Factor
USING: accessors assocs combinators deques dlists formatting fry
generalizations io kernel make math math.functions math.order
prettyprint sequences tools.memory.private ;
IN: rosetta-code.humble-numbers
TUPLE: humble-iterator 2s 3s 5s 7s digits
{ #digits initial: 1 } { target initial: 10 } ;
: <humble-iterator> ( -- humble-iterator )
humble-iterator new
1 1dlist >>2s
1 1dlist >>3s
1 1dlist >>5s
1 1dlist >>7s
H{ } clone >>digits ;
: enqueue ( n humble-iterator -- )
{
[ [ 2 * ] [ 2s>> ] ]
[ [ 3 * ] [ 3s>> ] ]
[ [ 5 * ] [ 5s>> ] ]
[ [ 7 * ] [ 7s>> ] ]
} [ bi* push-back ] map-compose 2cleave ;
: count-digits ( humble-iterator n -- )
[ over target>> >=
[ [ 1 + ] change-#digits [ 10 * ] change-target ] when ]
[ drop 1 swap [ #digits>> ] [ digits>> ] bi at+ ] bi ;
: ?pop ( 2s 3s 5s 7s n -- )
'[ dup peek-front _ = [ pop-front* ] [ drop ] if ] 4 napply ;
: next ( humble-iterator -- n )
dup dup { [ 2s>> ] [ 3s>> ] [ 5s>> ] [ 7s>> ] } cleave
4 ndup [ peek-front ] 4 napply min min min
{ [ ?pop ] [ swap enqueue ] [ count-digits ] [ ] } cleave ;
: upto-n-digits ( humble-iterator n -- seq )
1 + swap [ [ 2dup digits>> key? ] [ dup next , ] until ] { }
make [ digits>> delete-at ] dip but-last-slice ;
: .first50 ( seq -- )
"First 50 humble numbers:" print 50 head [ pprint bl ] each
nl ;
: .digit-breakdown ( humble-iterator -- )
"The digit counts of humble numbers:" print digits>> [
commas swap dup 1 = "" "s" ? "%9s have %2d digit%s\n"
printf
] assoc-each ;
: humble-numbers ( -- )
[ <humble-iterator> dup 95 upto-n-digits
[ .first50 nl ] [ drop .digit-breakdown nl ] [
"Total number of humble numbers found: " write length
commas print
] tri ] time ;
MAIN: humble-numbers
{{out}}
First 50 humble numbers:
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
The digit counts of humble numbers:
9 have 1 digit
36 have 2 digits
95 have 3 digits
197 have 4 digits
356 have 5 digits
579 have 6 digits
882 have 7 digits
1,272 have 8 digits
1,767 have 9 digits
2,381 have 10 digits
3,113 have 11 digits
3,984 have 12 digits
5,002 have 13 digits
6,187 have 14 digits
7,545 have 15 digits
9,081 have 16 digits
10,815 have 17 digits
12,759 have 18 digits
14,927 have 19 digits
17,323 have 20 digits
19,960 have 21 digits
22,853 have 22 digits
26,015 have 23 digits
29,458 have 24 digits
33,188 have 25 digits
37,222 have 26 digits
41,568 have 27 digits
46,245 have 28 digits
51,254 have 29 digits
56,618 have 30 digits
62,338 have 31 digits
68,437 have 32 digits
74,917 have 33 digits
81,793 have 34 digits
89,083 have 35 digits
96,786 have 36 digits
104,926 have 37 digits
113,511 have 38 digits
122,546 have 39 digits
132,054 have 40 digits
142,038 have 41 digits
152,515 have 42 digits
163,497 have 43 digits
174,986 have 44 digits
187,004 have 45 digits
199,565 have 46 digits
212,675 have 47 digits
226,346 have 48 digits
240,590 have 49 digits
255,415 have 50 digits
270,843 have 51 digits
286,880 have 52 digits
303,533 have 53 digits
320,821 have 54 digits
338,750 have 55 digits
357,343 have 56 digits
376,599 have 57 digits
396,533 have 58 digits
417,160 have 59 digits
438,492 have 60 digits
460,533 have 61 digits
483,307 have 62 digits
506,820 have 63 digits
531,076 have 64 digits
556,104 have 65 digits
581,902 have 66 digits
608,483 have 67 digits
635,864 have 68 digits
664,053 have 69 digits
693,065 have 70 digits
722,911 have 71 digits
753,593 have 72 digits
785,141 have 73 digits
817,554 have 74 digits
850,847 have 75 digits
885,037 have 76 digits
920,120 have 77 digits
956,120 have 78 digits
993,058 have 79 digits
1,030,928 have 80 digits
1,069,748 have 81 digits
1,109,528 have 82 digits
1,150,287 have 83 digits
1,192,035 have 84 digits
1,234,774 have 85 digits
1,278,527 have 86 digits
1,323,301 have 87 digits
1,369,106 have 88 digits
1,415,956 have 89 digits
1,463,862 have 90 digits
1,512,840 have 91 digits
1,562,897 have 92 digits
1,614,050 have 93 digits
1,666,302 have 94 digits
1,719,669 have 95 digits
Total number of humble numbers found: 41,990,065
Running time: 335.1803624581294 seconds
Go
Not particularly fast and uses a lot of memory but easier to understand than the 'log' based methods for generating 7-smooth numbers.
package main import ( "fmt" "math/big" ) var ( one = new(big.Int).SetUint64(1) two = new(big.Int).SetUint64(2) three = new(big.Int).SetUint64(3) five = new(big.Int).SetUint64(5) seven = new(big.Int).SetUint64(7) ten = new(big.Int).SetUint64(10) ) func min(a, b *big.Int) *big.Int { if a.Cmp(b) < 0 { return a } return b } func humble(n int) []*big.Int { h := make([]*big.Int, n) h[0] = new(big.Int).Set(one) next2, next3 := new(big.Int).Set(two), new(big.Int).Set(three) next5, next7 := new(big.Int).Set(five), new(big.Int).Set(seven) var i, j, k, l int for m := 1; m < len(h); m++ { h[m] = new(big.Int).Set(min(next2, min(next3, min(next5, next7)))) if h[m].Cmp(next2) == 0 { i++ next2.Mul(two, h[i]) } if h[m].Cmp(next3) == 0 { j++ next3.Mul(three, h[j]) } if h[m].Cmp(next5) == 0 { k++ next5.Mul(five, h[k]) } if h[m].Cmp(next7) == 0 { l++ next7.Mul(seven, h[l]) } } return h } func commatize(n int) string { s := fmt.Sprintf("%d", n) le := len(s) for i := le - 3; i >= 1; i -= 3 { s = s[0:i] + "," + s[i:] } return s } func main() { const n = 13 * 1e6 // calculate the first 13 million humble numbers, say h := humble(n) fmt.Println("The first 50 humble numbers are:") fmt.Println(h[0:50]) maxDigits := len(h[len(h)-1].String()) - 1 counts := make([]int, maxDigits+1) var maxUsed int digits := 1 pow10 := new(big.Int).Set(ten) for i := 0; i < len(h); i++ { for { if h[i].Cmp(pow10) >= 0 { pow10.Mul(pow10, ten) digits++ } else { break } } if digits > maxDigits { maxUsed = i break } counts[digits]++ } fmt.Printf("\nOf the first %s humble numbers:\n", commatize(maxUsed)) for i := 1; i <= maxDigits; i++ { s := "s" if i == 1 { s = "" } fmt.Printf("%9s have %2d digit%s\n", commatize(counts[i]), i, s) } }
{{out}}
The first 50 humble numbers are:
[1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120]
Of the first 12,591,874 humble numbers:
9 have 1 digit
36 have 2 digits
95 have 3 digits
197 have 4 digits
356 have 5 digits
579 have 6 digits
882 have 7 digits
1,272 have 8 digits
1,767 have 9 digits
2,381 have 10 digits
3,113 have 11 digits
3,984 have 12 digits
5,002 have 13 digits
6,187 have 14 digits
7,545 have 15 digits
9,081 have 16 digits
10,815 have 17 digits
12,759 have 18 digits
14,927 have 19 digits
17,323 have 20 digits
19,960 have 21 digits
22,853 have 22 digits
26,015 have 23 digits
29,458 have 24 digits
33,188 have 25 digits
37,222 have 26 digits
41,568 have 27 digits
46,245 have 28 digits
51,254 have 29 digits
56,618 have 30 digits
62,338 have 31 digits
68,437 have 32 digits
74,917 have 33 digits
81,793 have 34 digits
89,083 have 35 digits
96,786 have 36 digits
104,926 have 37 digits
113,511 have 38 digits
122,546 have 39 digits
132,054 have 40 digits
142,038 have 41 digits
152,515 have 42 digits
163,497 have 43 digits
174,986 have 44 digits
187,004 have 45 digits
199,565 have 46 digits
212,675 have 47 digits
226,346 have 48 digits
240,590 have 49 digits
255,415 have 50 digits
270,843 have 51 digits
286,880 have 52 digits
303,533 have 53 digits
320,821 have 54 digits
338,750 have 55 digits
357,343 have 56 digits
376,599 have 57 digits
396,533 have 58 digits
417,160 have 59 digits
438,492 have 60 digits
460,533 have 61 digits
483,307 have 62 digits
506,820 have 63 digits
531,076 have 64 digits
556,104 have 65 digits
581,902 have 66 digits
608,483 have 67 digits
635,864 have 68 digits
664,053 have 69 digits
693,065 have 70 digits
Julia
To spare heap memory, keeps only the last 2 million values found for use in the generation of further values.
function counthumbledigits(maxdigits, returnsequencelength=50) n, count, adjustindex, maxdiff = BigInt(1), 0, BigInt(0), 0 humble, savesequence = Vector{BigInt}([1]), Vector{BigInt}() base2, base3, base5, base7 = 1, 1, 1, 1 next2, next3, next5, next7 = BigInt(2), BigInt(3), BigInt(5), BigInt(7) digitcounts= Dict{Int, Int}(1 => 1) while n < BigInt(10)^(maxdigits+1) n = min(next2, next3, next5, next7) push!(humble, n) count += 1 if count == returnsequencelength savesequence = deepcopy(humble[1:returnsequencelength]) elseif count > 2000000 popfirst!(humble) adjustindex += 1 end placesbase10 = length(string(n)) if haskey(digitcounts, placesbase10) digitcounts[placesbase10] += 1 else digitcounts[placesbase10] = 1 end maxdiff = max(maxdiff, count - base2, count - base3, count - base5, count - base7) (next2 <= n) && (next2 = 2 * humble[(base2 += 1) - adjustindex]) (next3 <= n) && (next3 = 3 * humble[(base3 += 1) - adjustindex]) (next5 <= n) && (next5 = 5 * humble[(base5 += 1) - adjustindex]) (next7 <= n) && (next7 = 7 * humble[(base7 += 1) - adjustindex]) end savesequence, digitcounts, count, maxdiff end counthumbledigits(3) @time first120, digitcounts, count, maxdiff = counthumbledigits(99) println("\nTotal humble numbers counted: $count") println("Maximum depth between top of array and a multiplier: $maxdiff\n") println("The first 50 humble numbers are: $first120\n\nDigit counts of humble numbers:") for ndigits in sort(collect(keys(digitcounts)))[1:end-1] println(lpad(digitcounts[ndigits], 10), " have ", lpad(ndigits, 3), " digits.") end
{{out}}
828.693164 seconds (3.61 G allocations: 64.351 GiB, 51.37% gc time)
Total humble numbers counted: 51428827
Maximum depth between top of array and a multiplier: 1697189
The first 50 humble numbers are: BigInt[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120]
Digit counts of humble numbers:
9 have 1 digits.
36 have 2 digits.
95 have 3 digits.
197 have 4 digits.
356 have 5 digits.
579 have 6 digits.
882 have 7 digits.
1272 have 8 digits.
1767 have 9 digits.
2381 have 10 digits.
3113 have 11 digits.
3984 have 12 digits.
5002 have 13 digits.
6187 have 14 digits.
7545 have 15 digits.
9081 have 16 digits.
10815 have 17 digits.
12759 have 18 digits.
14927 have 19 digits.
17323 have 20 digits.
19960 have 21 digits.
22853 have 22 digits.
26015 have 23 digits.
29458 have 24 digits.
33188 have 25 digits.
37222 have 26 digits.
41568 have 27 digits.
46245 have 28 digits.
51254 have 29 digits.
56618 have 30 digits.
62338 have 31 digits.
68437 have 32 digits.
74917 have 33 digits.
81793 have 34 digits.
89083 have 35 digits.
96786 have 36 digits.
104926 have 37 digits.
113511 have 38 digits.
122546 have 39 digits.
132054 have 40 digits.
142038 have 41 digits.
152515 have 42 digits.
163497 have 43 digits.
174986 have 44 digits.
187004 have 45 digits.
199565 have 46 digits.
212675 have 47 digits.
226346 have 48 digits.
240590 have 49 digits.
255415 have 50 digits.
270843 have 51 digits.
286880 have 52 digits.
303533 have 53 digits.
320821 have 54 digits.
338750 have 55 digits.
357343 have 56 digits.
376599 have 57 digits.
396533 have 58 digits.
417160 have 59 digits.
438492 have 60 digits.
460533 have 61 digits.
483307 have 62 digits.
506820 have 63 digits.
531076 have 64 digits.
556104 have 65 digits.
581902 have 66 digits.
608483 have 67 digits.
635864 have 68 digits.
664053 have 69 digits.
693065 have 70 digits.
722911 have 71 digits.
753593 have 72 digits.
785141 have 73 digits.
817554 have 74 digits.
850847 have 75 digits.
885037 have 76 digits.
920120 have 77 digits.
956120 have 78 digits.
993058 have 79 digits.
1030928 have 80 digits.
1069748 have 81 digits.
1109528 have 82 digits.
1150287 have 83 digits.
1192035 have 84 digits.
1234774 have 85 digits.
1278527 have 86 digits.
1323301 have 87 digits.
1369106 have 88 digits.
1415956 have 89 digits.
1463862 have 90 digits.
1512840 have 91 digits.
1562897 have 92 digits.
1614050 have 93 digits.
1666302 have 94 digits.
1719669 have 95 digits.
1774166 have 96 digits.
1829805 have 97 digits.
1886590 have 98 digits.
1944540 have 99 digits.
2003661 have 100 digits.
Kotlin
fun isHumble(i: Int): Boolean { if (i <= 1) return true if (i % 2 == 0) return isHumble(i / 2) if (i % 3 == 0) return isHumble(i / 3) if (i % 5 == 0) return isHumble(i / 5) if (i % 7 == 0) return isHumble(i / 7) return false } fun main() { val limit: Int = Short.MAX_VALUE.toInt() val humble = mutableMapOf<Int, Int>() var count = 0 var num = 1 while (count < limit) { if (isHumble(num)) { val str = num.toString() val len = str.length humble.merge(len, 1) { a, b -> a + b } if (count < 50) print("$num ") count++ } num++ } println("\n") println("Of the first $count humble numbers:") num = 1 while (num < humble.size - 1) { if (humble.containsKey(num)) { val c = humble[num] println("%5d have %2d digits".format(c, num)) num++ } else { break } } }
{{out}}
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
Of the first 32767 humble numbers:
9 have 1 digits
36 have 2 digits
95 have 3 digits
197 have 4 digits
356 have 5 digits
579 have 6 digits
882 have 7 digits
1272 have 8 digits
1767 have 9 digits
Perl
use strict; use warnings; use List::Util 'min'; #use bigint # works, but slow use Math::GMPz; # this module gives roughly 16x speed-up sub humble_gen { my @s = ([1], [1], [1], [1]); my @m = (2, 3, 5, 7); @m = map { Math::GMPz->new($_) } @m; # comment out to NOT use Math::GMPz return sub { my $n = min $s[0][0], $s[1][0], $s[2][0], $s[3][0]; for (0..3) { shift @{$s[$_]} if $s[$_][0] == $n; push @{$s[$_]}, $n * $m[$_] } return $n } } my $h = humble_gen; my $i = 0; my $upto = 50; my $list; ++$i, $list .= $h->(). " " until $i == $upto; print "$list\n"; $h = humble_gen; # from the top... my $count = 0; my $digits = 1; while ($digits <= $upto) { ++$count and next if $digits == length $h->(); printf "Digits: %2d - Count: %s\n", $digits++, $count; $count = 1; }
{{out}}
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
Digits: 1 - Count: 9
Digits: 2 - Count: 36
Digits: 3 - Count: 95
Digits: 4 - Count: 197
Digits: 5 - Count: 356
Digits: 6 - Count: 579
Digits: 7 - Count: 882
Digits: 8 - Count: 1272
Digits: 9 - Count: 1767
Digits: 10 - Count: 2381
Digits: 11 - Count: 3113
Digits: 12 - Count: 3984
Digits: 13 - Count: 5002
Digits: 14 - Count: 6187
Digits: 15 - Count: 7545
Digits: 16 - Count: 9081
Digits: 17 - Count: 10815
Digits: 18 - Count: 12759
Digits: 19 - Count: 14927
Digits: 20 - Count: 17323
Digits: 21 - Count: 19960
Digits: 22 - Count: 22853
Digits: 23 - Count: 26015
Digits: 24 - Count: 29458
Digits: 25 - Count: 33188
Digits: 26 - Count: 37222
Digits: 27 - Count: 41568
Digits: 28 - Count: 46245
Digits: 29 - Count: 51254
Digits: 30 - Count: 56618
Digits: 31 - Count: 62338
Digits: 32 - Count: 68437
Digits: 33 - Count: 74917
Digits: 34 - Count: 81793
Digits: 35 - Count: 89083
Digits: 36 - Count: 96786
Digits: 37 - Count: 104926
Digits: 38 - Count: 113511
Digits: 39 - Count: 122546
Digits: 40 - Count: 132054
Digits: 41 - Count: 142038
Digits: 42 - Count: 152515
Digits: 43 - Count: 163497
Digits: 44 - Count: 174986
Digits: 45 - Count: 187004
Digits: 46 - Count: 199565
Digits: 47 - Count: 212675
Digits: 48 - Count: 226346
Digits: 49 - Count: 240590
Digits: 50 - Count: 255415
```
## Perl 6
{{works with|Rakudo|2019.07.1}}
```perl6
sub smooth-numbers (*@list) {
cache my \Smooth := gather {
my %i = (flat @list) Z=> (Smooth.iterator for ^@list);
my %n = (flat @list) Z=> 1 xx *;
loop {
take my $n := %n{*}.min;
for @list -> \k {
%n{k} = %i{k}.pull-one * k if %n{k} == $n;
}
}
}
}
my $humble := smooth-numbers(2,3,5,7);
put $humble[^50];
say '';
my $upto = 50;
my $digits = 1;
my $count;
$humble.map: -> \h {
++$count and next if h.chars == $digits;
printf "Digits: %2d - Count: %s\n", $digits++, $count;
$count = 1;
last if $digits > $upto;
}
```
{{out}}
```txt
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
Digits: 1 - Count: 9
Digits: 2 - Count: 36
Digits: 3 - Count: 95
Digits: 4 - Count: 197
Digits: 5 - Count: 356
Digits: 6 - Count: 579
Digits: 7 - Count: 882
Digits: 8 - Count: 1272
Digits: 9 - Count: 1767
Digits: 10 - Count: 2381
Digits: 11 - Count: 3113
Digits: 12 - Count: 3984
Digits: 13 - Count: 5002
Digits: 14 - Count: 6187
Digits: 15 - Count: 7545
Digits: 16 - Count: 9081
Digits: 17 - Count: 10815
Digits: 18 - Count: 12759
Digits: 19 - Count: 14927
Digits: 20 - Count: 17323
Digits: 21 - Count: 19960
Digits: 22 - Count: 22853
Digits: 23 - Count: 26015
Digits: 24 - Count: 29458
Digits: 25 - Count: 33188
Digits: 26 - Count: 37222
Digits: 27 - Count: 41568
Digits: 28 - Count: 46245
Digits: 29 - Count: 51254
Digits: 30 - Count: 56618
Digits: 31 - Count: 62338
Digits: 32 - Count: 68437
Digits: 33 - Count: 74917
Digits: 34 - Count: 81793
Digits: 35 - Count: 89083
Digits: 36 - Count: 96786
Digits: 37 - Count: 104926
Digits: 38 - Count: 113511
Digits: 39 - Count: 122546
Digits: 40 - Count: 132054
Digits: 41 - Count: 142038
Digits: 42 - Count: 152515
Digits: 43 - Count: 163497
Digits: 44 - Count: 174986
Digits: 45 - Count: 187004
Digits: 46 - Count: 199565
Digits: 47 - Count: 212675
Digits: 48 - Count: 226346
Digits: 49 - Count: 240590
Digits: 50 - Count: 255415
```
## Phix
{{libheader|mpfr}}
{{trans|Julia}}
I felt pretty good about the performance of this, until I ran the Go version - humbled indeed!
It will go all the way to 100 digits if you give it time (18 mins, on 64bit - 32bit runs out of memory after printing the 99th line)
I also tried a log version (similar to [[Hamming_numbers#A_much_faster_logarithmic_version|Hamming_numbers]]) but inaccuracies with floor(h[n][LOG]) crept in quite early, at just 10 digits.
```Phix
-- demo/rosetta/humble.exw
include mpfr.e
procedure humble(integer n, bool countdigits=false)
-- if countdigits is false: show first n humble numbers,
-- if countdigits is true: count them up to n digits.
sequence humble = {mpz_init(1)},
nexts = {2,3,5,7},
indices = repeat(1,4)
for i=1 to 4 do nexts[i] = mpz_init(nexts[i]) end for
integer digits = 1,
count = 1,
dead = 1,
tc = 0
atom t0 = time()
mpz p10 = mpz_init(10)
while ((not countdigits) and length(humble)=0 then
mpz_mul_si(p10,p10,10)
integer d = min(indices)
for k=dead to d-1 do
humble[k] = mpz_free(humble[k])
end for
dead = d
string s = iff(digits=1?"":"s"),
e = elapsed(time()-t0)
tc += count
-- e &= sprintf(", %,d dead",{dead-1})
e &= sprintf(", total:%,d",{tc})
printf(1,"%,12d humble numbers have %d digit%s (%s)\n",{count,digits,s,e})
digits += 1
count = 1
else
count += 1
end if
end if
for j=1 to 4 do
if mpz_cmp(nexts[j],x)<=0 then
indices[j] += 1
mpz_mul_si(nexts[j],humble[indices[j]],get_prime(j))
end if
end for
end while
if not countdigits then
for i=1 to length(humble) do
humble[i] = shorten(mpz_get_str(humble[i]),ml:=10)
end for
printf(1,"First %d humble numbers: %s\n\n",{n,join(humble," ")})
end if
end procedure
humble(50)
humble(42,true)
```
{{out}}
```txt
First 50 humble numbers: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
9 humble numbers have 1 digit (0s, total:9)
36 humble numbers have 2 digits (0s, total:45)
95 humble numbers have 3 digits (0s, total:140)
197 humble numbers have 4 digits (0s, total:337)
356 humble numbers have 5 digits (0s, total:693)
579 humble numbers have 6 digits (0.0s, total:1,272)
882 humble numbers have 7 digits (0.0s, total:2,154)
1,272 humble numbers have 8 digits (0.0s, total:3,426)
1,767 humble numbers have 9 digits (0.1s, total:5,193)
2,381 humble numbers have 10 digits (0.1s, total:7,574)
3,113 humble numbers have 11 digits (0.2s, total:10,687)
3,984 humble numbers have 12 digits (0.2s, total:14,671)
5,002 humble numbers have 13 digits (0.3s, total:19,673)
6,187 humble numbers have 14 digits (0.4s, total:25,860)
7,545 humble numbers have 15 digits (0.5s, total:33,405)
9,081 humble numbers have 16 digits (0.6s, total:42,486)
10,815 humble numbers have 17 digits (0.8s, total:53,301)
12,759 humble numbers have 18 digits (0.9s, total:66,060)
14,927 humble numbers have 19 digits (1.2s, total:80,987)
17,323 humble numbers have 20 digits (1.4s, total:98,310)
19,960 humble numbers have 21 digits (1.7s, total:118,270)
22,853 humble numbers have 22 digits (2.0s, total:141,123)
26,015 humble numbers have 23 digits (2.3s, total:167,138)
29,458 humble numbers have 24 digits (2.7s, total:196,596)
33,188 humble numbers have 25 digits (3.2s, total:229,784)
37,222 humble numbers have 26 digits (3.7s, total:267,006)
41,568 humble numbers have 27 digits (4.3s, total:308,574)
46,245 humble numbers have 28 digits (5.0s, total:354,819)
51,254 humble numbers have 29 digits (5.7s, total:406,073)
56,618 humble numbers have 30 digits (6.5s, total:462,691)
62,338 humble numbers have 31 digits (7.3s, total:525,029)
68,437 humble numbers have 32 digits (8.3s, total:593,466)
74,917 humble numbers have 33 digits (9.4s, total:668,383)
81,793 humble numbers have 34 digits (10.5s, total:750,176)
89,083 humble numbers have 35 digits (11.7s, total:839,259)
96,786 humble numbers have 36 digits (13.1s, total:936,045)
104,926 humble numbers have 37 digits (14.6s, total:1,040,971)
113,511 humble numbers have 38 digits (16.2s, total:1,154,482)
122,546 humble numbers have 39 digits (17.9s, total:1,277,028)
132,054 humble numbers have 40 digits (19.7s, total:1,409,082)
142,038 humble numbers have 41 digits (21.7s, total:1,551,120)
152,515 humble numbers have 42 digits (23.9s, total:1,703,635)
```
## Racket
{{trans|Go}}
```racket
#lang racket
(define (gen-humble-numbers N (kons #f) (k0 (void)))
(define rv (make-vector N 1))
(define (loop n 2-idx 3-idx 5-idx 7-idx next-2 next-3 next-5 next-7 k)
(if (= n N)
rv
(let ((mn (min next-2 next-3 next-5 next-7)))
(vector-set! rv n mn)
(define (add-1-if-min n x) (if (= mn n) (add1 x) x))
(define (*vr.i-if-min n m i) (if (= mn n) (* m (vector-ref rv i)) n))
(let* ((2-idx (add-1-if-min next-2 2-idx))
(next-2 (*vr.i-if-min next-2 2 2-idx))
(3-idx (add-1-if-min next-3 3-idx))
(next-3 (*vr.i-if-min next-3 3 3-idx))
(5-idx (add-1-if-min next-5 5-idx))
(next-5 (*vr.i-if-min next-5 5 5-idx))
(7-idx (add-1-if-min next-7 7-idx))
(next-7 (*vr.i-if-min next-7 7 7-idx))
(k (and kons (kons mn k))))
(loop (add1 n) 2-idx 3-idx 5-idx 7-idx next-2 next-3 next-5 next-7 k)))))
(loop 1 0 0 0 0 2 3 5 7 (and kons (kons 1 k0))))
(define ((digit-tracker breaker) h last-ten.count)
(let ((last-ten (car last-ten.count)))
(if (< h last-ten)
(cons last-ten (add1 (cdr last-ten.count)))
(begin
(printf "~a humble numbers with ~a digits~%" (cdr last-ten.count) (order-of-magnitude last-ten))
(cons (breaker (* 10 last-ten)) 1)))))
(define (Humble-numbers)
(displayln (gen-humble-numbers 50))
(time
(let/ec break
(void (gen-humble-numbers
100000000
(digit-tracker (λ (o) (if (> (order-of-magnitude o) 100) (break) o)))
'(10 . 0))))))
(module+ main
(Humble-numbers))
```
{{out}}
output has been elided manually, to avoid repetition with the numbers you've already seen elsewhere:
```txt
#(1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120)
9 humble numbers with 1 digits
36 humble numbers with 2 digits
95 humble numbers with 3 digits
197 humble numbers with 4 digits
356 humble numbers with 5 digits
579 humble numbers with 6 digits
882 humble numbers with 7 digits
1272 humble numbers with 8 digits
1767 humble numbers with 9 digits
2381 humble numbers with 10 digits
...
17323 humble numbers with 20 digits
...
56618 humble numbers with 30 digits
...
132054 humble numbers with 40 digits
...
255415 humble numbers with 50 digits
...
438492 humble numbers with 60 digits
...
693065 humble numbers with 70 digits
...
1030928 humble numbers with 80 digits
...
1463862 humble numbers with 90 digits
...
2003661 humble numbers with 100 digits
cpu time: 234970 real time: 235489 gc time: 189187
```
## REXX
```rexx
/*REXX program computes and displays humble numbers, also will display counts of sizes.*/
parse arg n m . /*obtain optional arguments from the CL*/
if n=='' | n=="," then n= 50 /*Not specified? Then use the default.*/
if m=='' | m=="," then m= 60 /* " " " " " " */
numeric digits 1 + max(20, m) /*be able to handle some big numbers. */
$.= 0 /*a count array for X digit humble #s*/
call humble n; list= /*call HUMBLE sub; initialize the list.*/
do j=1 for n; list= list @.j /*append a humble number to the list.*/
end /*j*/
if list\='' then do; say "A list of the first " n ' humble numbers are:'
say strip(list) /*elide the leading blank in the list. */
end
say
call humble -m /*invoke subroutine for counting nums. */
if $.1==0 then exit /*if no counts, then we're all finished*/
total= 0 /*initialize count of humble numbers. */
$.1= $.1 + 1 /*adjust count for absent 1st humble #.*/
say ' The digit counts of humble numbers:'
say ' ═════════════════════════════════════════'
do c=1 while $.c>0; s= left('s', length($.c)>1) /*count needs pluralization?*/
say right( commas($.c), 30) ' have ' right(c, 2) " digit"s
total= total + $.c /* ◄─────────────────────────────────┐ */
end /*k*/ /*bump humble number count (so far)──┘ */
/*REXX program computes and displays humble numbers, also will display a count of sizes.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: procedure; arg _; do i=length(_)-3 to 1 by -3; _=insert(',', _, i); end; return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
humble: procedure expose @. $.; parse arg x; if x==0 then return
y= abs(x); a= y; noCount= x>0; if x<0 then y= 999999999
#2= 1; #3= 1; #5= 1; #7= 1 /*define the initial humble constants. */
$.= 0; @.= 0; @.1= 1 /*initialize counts and humble numbers.*/
do h=2 for y-1
@.h= min(2*@.#2,3*@.#3,5*@.#5,7*@.#7) /*pick the minimum of 4 humble numbers.*/
m= @.h /*M: " " " " " " */
if 2*@.#2 == m then #2 = #2 + 1 /*Is number already defined? Use next #*/
if 3*@.#3 == m then #3 = #3 + 1 /* " " " " " " "*/
if 5*@.#5 == m then #5 = #5 + 1 /* " " " " " " "*/
if 7*@.#7 == m then #7 = #7 + 1 /* " " " " " " "*/
if noCount then iterate /*Not counting digits? Then iterate. */
L= length(m); if L>a then leave /*Are we done with counting? Then quit*/
$.L= $.L + 1 /*bump the digit count for this number.*/
end /*h*/ /*the humble numbers are in the @ array*/
return /* " count results " " " $ " */
```
{{out|output|text= when using the default inputs:}}
```txt
A list of the first 50 humble numbers are:
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
The digit counts of humble numbers:
═════════════════════════════════════════
9 have 1 digit
36 have 2 digits
95 have 3 digits
197 have 4 digits
356 have 5 digits
579 have 6 digits
882 have 7 digits
1,272 have 8 digits
1,767 have 9 digits
2,381 have 10 digits
3,113 have 11 digits
3,984 have 12 digits
5,002 have 13 digits
6,187 have 14 digits
7,545 have 15 digits
9,081 have 16 digits
10,815 have 17 digits
12,759 have 18 digits
14,927 have 19 digits
17,323 have 20 digits
19,960 have 21 digits
22,853 have 22 digits
26,015 have 23 digits
29,458 have 24 digits
33,188 have 25 digits
37,222 have 26 digits
41,568 have 27 digits
46,245 have 28 digits
51,254 have 29 digits
56,618 have 30 digits
62,338 have 31 digits
68,437 have 32 digits
74,917 have 33 digits
81,793 have 34 digits
89,083 have 35 digits
96,786 have 36 digits
104,926 have 37 digits
113,511 have 38 digits
122,546 have 39 digits
132,054 have 40 digits
142,038 have 41 digits
152,515 have 42 digits
163,497 have 43 digits
174,986 have 44 digits
187,004 have 45 digits
199,565 have 46 digits
212,675 have 47 digits
226,346 have 48 digits
240,590 have 49 digits
255,415 have 50 digits
270,843 have 51 digits
286,880 have 52 digits
303,533 have 53 digits
320,821 have 54 digits
338,750 have 55 digits
357,343 have 56 digits
376,599 have 57 digits
396,533 have 58 digits
417,160 have 59 digits
438,492 have 60 digits
total number of humble numbers found: 6,870,667
```
## Sidef
```ruby
func smooth_generator(primes) {
var s = primes.len.of { [1] }
{
var n = s.map { .first }.min
{ |i|
s[i].shift if (s[i][0] == n)
s[i] << (n * primes[i])
} * primes.len
n
}
}
with (smooth_generator([2,3,5,7])) {|g|
say 50.of { g.run }.join(' ')
}
say "\nThe digit counts of humble numbers"
say '═'*35
with (smooth_generator([2,3,5,7])) {|g|
for (var(d=1,c=0); d <= 20; ++c) {
var n = g.run
n.len > d || next
say "#{'%10s'%c.commify} have #{'%2d'%d} digit#{[:s,''][d==1]}"
(c, d) = (0, n.len)
}
}
```
{{out}}
```txt
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
The digit counts of humble numbers
═══════════════════════════════════
9 have 1 digit
36 have 2 digits
95 have 3 digits
197 have 4 digits
356 have 5 digits
579 have 6 digits
882 have 7 digits
1,272 have 8 digits
1,767 have 9 digits
2,381 have 10 digits
3,113 have 11 digits
3,984 have 12 digits
5,002 have 13 digits
6,187 have 14 digits
7,545 have 15 digits
9,081 have 16 digits
10,815 have 17 digits
12,759 have 18 digits
14,927 have 19 digits
17,323 have 20 digits
```
## zkl
{{trans|Go}}
{{libheader|GMP}} GNU Multiple Precision Arithmetic Library
```zkl
var [const] BI=Import("zklBigNum"); // libGMP
var one = BI(1), two = BI(2), three = BI(3),
five = BI(5), seven = BI(7);
fcn humble(n){ // --> List of BigInt Humble numbers
h:=List.createLong(n); h.append(one);
next2,next3 := two.copy(), three.copy();
next5,next7 := five.copy(), seven.copy();
reg i=0,j=0,k=0,l=0;
do(n-1){
h.append( hm:=BI(next2.min(next3.min(next5.min(next7)))) );
if(hm==next2) next2.set(two) .mul(h[i+=1]);
if(hm==next3) next3.set(three).mul(h[j+=1]);
if(hm==next5) next5.set(five) .mul(h[k+=1]);
if(hm==next7) next7.set(seven).mul(h[l+=1]);
}
h
}
```
```zkl
fcn __main__{
const N = 5 * 1e6; // calculate the first 1 million humble numbers, say
h:=humble(N);
println("The first 50 humble numbers are:\n ",h[0,50].concat(" "));
counts:=Dictionary(); // tally the number of digits in each number
h.apply2('wrap(n){ counts.incV(n.numDigits) });
println("\nOf the first %,d humble numbers:".fmt(h.len()));
println("Digits Count");
foreach n in (counts.keys.apply("toInt").sort()){
println("%2d %,9d".fmt(n,counts[n], n));
}
}
```
{{out}}
The first 50 humble numbers are:
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 50 54 56 60 63 64 70 72 75 80 81 84 90 96 98 100 105 108 112 120
Of the first 5,000,000 humble numbers:
Digits Count
1 9
2 36
3 95
4 197
5 356
6 579
7 882
8 1,272
9 1,767
10 2,381
11 3,113
12 3,984
13 5,002
14 6,187
15 7,545
16 9,081
17 10,815
18 12,759
19 14,927
20 17,323
21 19,960
22 22,853
23 26,015
24 29,458
25 33,188
26 37,222
27 41,568
28 46,245
29 51,254
30 56,618
31 62,338
32 68,437
33 74,917
34 81,793
35 89,083
36 96,786
37 104,926
38 113,511
39 122,546
40 132,054
41 142,038
42 152,515
43 163,497
44 174,986
45 187,004
46 199,565
47 212,675
48 226,346
49 240,590
50 255,415
51 270,843
52 286,880
53 303,533
54 320,821
55 338,750
56 115,460
```