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Odd squarefree semiprimes: Difference between revisions

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Odd squarefree semiprimes (view source)

Revision as of 09:13, 8 January 2024

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817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979 985 989 993 995
</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">n = 1000; primes = Most@NestWhileList[NextPrime, 3, # < n/3 &];
reduceList[x_List, n_] := TakeWhile[Rest[x], # < n/First[x] &];
q = Rest /@
NestWhileList[reduceList[#, n] &, primes, Length@# > 2 &];
semiPrimes = Sort@Flatten@MapThread[Times, {q, primes[[;; Length@q]]}];
Partition[TakeWhile[semiPrimes, # < 1000 &], UpTo[10]] // TableForm</syntaxhighlight>
 
{{out}}<pre>
15 21 33 35 39 51 55 57 65 69
77 85 87 91 93 95 111 115 119 123
129 133 141 143 145 155 159 161 177 183
185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287
291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381
391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485
489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573
579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687
689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779
781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879
889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979
985 989 993 995
</pre>
 
Line 832 ⟶ 802:
 
Counted 194 odd squarefree semiprimes under 1000
</pre>
 
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">n = 1000; primes = Most@NestWhileList[NextPrime, 3, # < n/3 &];
reduceList[x_List, n_] := TakeWhile[Rest[x], # < n/First[x] &];
q = Rest /@
NestWhileList[reduceList[#, n] &, primes, Length@# > 2 &];
semiPrimes = Sort@Flatten@MapThread[Times, {q, primes[[;; Length@q]]}];
Partition[TakeWhile[semiPrimes, # < 1000 &], UpTo[10]] // TableForm</syntaxhighlight>
 
{{out}}<pre>
15 21 33 35 39 51 55 57 65 69
77 85 87 91 93 95 111 115 119 123
129 133 141 143 145 155 159 161 177 183
185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287
291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381
391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485
489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573
579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687
689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779
781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879
889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979
985 989 993 995
</pre>
 
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
block(
[count:0,oddsemiprime:[]],
while count<1000 do (
i:lambda([x],oddp(x) and length(ifactors(x))=2 and unique(map(second,ifactors(x)))=[1])(count),
if i then oddsemiprime:endcons(count,oddsemiprime),
count:count+1),
oddsemiprime);
</syntaxhighlight>
{{out}}
<pre>
[15,21,33,35,39,51,55,57,65,69,77,85,87,91,93,95,111,115,119,123,129,133,141,143,145,155,159,161,177,183,185,187,201,203,205,209,213,215,217,219,221,235,237,247,249,253,259,265,267,287,291,295,299,301,303,305,309,319,321,323,327,329,335,339,341,355,365,371,377,381,391,393,395,403,407,411,413,415,417,427,437,445,447,451,453,469,471,473,481,485,489,493,497,501,505,511,515,517,519,527,533,535,537,543,545,551,553,559,565,573,579,581,583,589,591,597,611,623,629,633,635,649,655,667,669,671,679,681,685,687,689,695,697,699,703,707,713,717,721,723,731,737,745,749,753,755,763,767,771,779,781,785,789,791,793,799,803,807,813,815,817,831,835,843,849,851,865,869,871,879,889,893,895,899,901,905,913,917,921,923,933,939,943,949,951,955,959,965,973,979,985,989,993,995]
</pre>
 
Line 921 ⟶ 937:
15, 21, 33, 35, 39, ..., 979, 985, 989, 993, 995
</pre>
=={{header|Prolog}}==
works with swi-prolog
<syntaxhighlight lang="prolog">
oddPrimes(3, Limit):- 3 =< Limit.
oddPrimes(N, Limit):-
between(5, Limit, N),
N /\ 1 > 0, % odd
N mod 3 > 0, % \= 3*i
M is floor(sqrt(N)) + 1, % reverse 6*I-1
Max is M div 6,
forall(between(1, Max, I), (N mod (6*I-1) > 0, N mod (6*I+1) > 0)).
 
merge([], Sort, Sort).
merge([X|Sort1], [Y|Sort2], [X|Sort]):-
X < Y,!,
merge(Sort1, [Y|Sort2], Sort).
merge(Sort1, [Y|Sort2], [Y|Sort]):-
merge(Sort2, Sort1, Sort).
 
semiPrimes(PList, Limit, SpList):-
semiPrimes(PList, Limit, [], SpList).
 
semiPrimes([], _, Acc, Acc). % odd, squarefree generator
semiPrimes([P|PList], Limit, Acc, SpList):-
findall(Sp, (member(X, PList), X =< Limit div P, Sp is P * X), MList),
MList = [_|_],!,
merge(Acc, MList, Acc1),
semiPrimes(PList, Limit, Acc1, SpList).
semiPrimes(_, _, Acc, Acc).
 
showList(List):-
findnsols(20, X, (member(X, List), writef('%4r', [X])), _SubList), nl,
fail.
showList(_).
do:-Limit is 1000,
PLimit is Limit div 3,
findall(N, oddPrimes(N, PLimit), PList),
semiPrimes(PList, Limit, SpList),!,
showList(SpList).
</syntaxhighlight>
{{out}}
<pre>
?- time(do).
15 21 33 35 39 51 55 57 65 69 77 85 87 91 93 95 111 115 119 123
129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979 985 989 993 995
% 11,306 inferences, 0.005 CPU in 0.006 seconds (85% CPU, 2410378 Lips)
true.
</pre>
 
=={{header|Python}}==
Line 1,125 ⟶ 1,197:
done...
</pre>
=={{header|RPL}}==
{{works with|HP|49}}
≪ → max
≪ { } 3
'''DO'''
3 1 CF
'''WHILE''' DUP2 > 1 FC? AND '''REPEAT'''
DUP2 *
'''IF''' DUP max ≤ '''THEN''' 4 ROLL + UNROT '''ELSE''' DROP 1 SF '''END'''
NEXTPRIME
'''END'''
DROP NEXTPRIME
'''UNTIL''' DUP 3 * max > '''END'''
DROP SORT
≫ ≫ '<span style="color:blue">OSSP</span>' STO
 
1000 <span style="color:blue">OSSP</span>
{{out}}
<pre>
1: {15 21 33 35 39 51 55 57 65 69 77 85 87 91 93 95 111 115 119 123 129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219 221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323 327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427 437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527 533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633 635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723 731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815 817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923 933 939 943 949 951 955 959 965 973 979 985 989 993 995}
</pre>
 
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">
require 'prime'
 
res = (1..1000).step(2).select {|n| n.prime_division.map(&:last) == [1, 1] }
res.each_slice(20){|slice| puts "%4d"*slice.size % slice}
puts "\nCount: #{res.count}"</syntaxhighlight>
{{out}}
<pre> 15 21 33 35 39 51 55 57 65 69 77 85 87 91 93 95 111 115 119 123
129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979 985 989 993 995
 
Count: 194
</pre>
 
=={{header|Scala}}==
Scala3 ready
Line 1,143 ⟶ 1,259:
}
 
def semiPrimes(limit: Int): Seq[Int] = { // odd and, squarefree generator
def iter(primeList: Seq[Int], acc: Seq[Int]): Seq[Int] = {
val (start, primeList1) = (primeList.head, primeList.tail)
Line 1,197 ⟶ 1,313:
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-seq}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./math" for Int
{{libheader|Wren-sort}}
<syntaxhighlight lang="ecmascript">import "./mathfmt" for IntFmt
import "/seq" for Lst
import "/fmt" for Fmt
import "/sort" for Sort
 
var primes = Int.primeSieve(333)
Line 1,214 ⟶ 1,326:
}
}
Sort.quick(oss)
System.print("Odd squarefree semiprimes under 1,000:")
Fmt.tprint("$3d", oss.sort(), 10)
for (chunk in Lst.chunks(oss, 10)) Fmt.print("$3d", chunk)
System.print("\n%(oss.count) such numbers found.")</syntaxhighlight>
 
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