Super-Poulet numbers: Difference between revisions
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{{draft task}} |
{{draft task}} |
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A [[wp:Super-Poulet_number| |
A [[wp:Super-Poulet_number|super-Poulet number]] is a [[wp:Fermat_pseudoprime|Poulet number]] (or Fermat pseudoprime to base 2) whose every divisor '''''d''''' evenly divides '''''2<sup>d</sup> − 2'''''. |
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;Task |
;Task |
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* Find and display the first '''20''' |
* Find and display the first '''20''' super-Poulet numbers. |
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;Stretch |
;Stretch |
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* Find and display the index and value of the first |
* Find and display the index and value of the first super-Poulet number greater than one million. |
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;See also |
;See also |
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;*[[Fermat pseudoprimes|Task: Fermat pseudoprimes]] |
;*[[Fermat pseudoprimes|Task: Fermat pseudoprimes]] |
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;*[[wp:Super-Poulet_number|Wikipedia: |
;*[[wp:Super-Poulet_number|Wikipedia: super-Poulet number]] |
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;*[[oeis:A050217|OEIS:A050217 - |
;*[[oeis:A050217|OEIS:A050217 - super-Poulet numbers]] |
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my @super-poulet = @poulet.grep: { all .&divisors.skip(1).map: { 2 == expmod 2, $_, $_ } } |
my @super-poulet = @poulet.grep: { all .&divisors.skip(1).map: { 2 == expmod 2, $_, $_ } } |
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say "First 20 |
say "First 20 super-Poulet numbers:\n" ~ @super-poulet[^20].gist; |
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for 1e6.Int, 1e7.Int -> $threshold { |
for 1e6.Int, 1e7.Int -> $threshold { |
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say "\nIndex and value of first |
say "\nIndex and value of first super-Poulet greater than {$threshold.&cardinal}:"; |
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my $index = @super-poulet.first: * > $threshold, :k; |
my $index = @super-poulet.first: * > $threshold, :k; |
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say "{(1+$index).&ordinal-digit} |
say "{(1+$index).&ordinal-digit} super-Poulet number == " ~ @super-poulet[$index]., |
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}</lang> |
}</lang> |
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{{out}} |
{{out}} |
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<pre>First 20 |
<pre>First 20 super-Poulet numbers: |
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(341 1387 2047 2701 3277 4033 4369 4681 5461 7957 8321 10261 13747 14491 15709 18721 19951 23377 31417 31609) |
(341 1387 2047 2701 3277 4033 4369 4681 5461 7957 8321 10261 13747 14491 15709 18721 19951 23377 31417 31609) |
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Index and value of first |
Index and value of first super-Poulet greater than one million: |
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109th |
109th super-Poulet number == 1,016,801 |
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Index and value of first |
Index and value of first super-Poulet greater than ten million: |
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317th |
317th super-Poulet number == 10,031,653 |
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</pre> |
</pre> |
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Revision as of 00:00, 17 August 2022
Super-Poulet numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A super-Poulet number is a Poulet number (or Fermat pseudoprime to base 2) whose every divisor d evenly divides 2d − 2.
- Task
- Find and display the first 20 super-Poulet numbers.
- Stretch
- Find and display the index and value of the first super-Poulet number greater than one million.
- See also
Raku
<lang perl6>use Prime::Factor; use Lingua::EN::Numbers;
my @poulet = lazy (2..*).hyper(:2000batch).grep: { !.is-prime && (1 == expmod 2, $_ - 1, $_) } my @super-poulet = @poulet.grep: { all .&divisors.skip(1).map: { 2 == expmod 2, $_, $_ } }
say "First 20 super-Poulet numbers:\n" ~ @super-poulet[^20].gist;
for 1e6.Int, 1e7.Int -> $threshold {
say "\nIndex and value of first super-Poulet greater than {$threshold.&cardinal}:";
my $index = @super-poulet.first: * > $threshold, :k;
say "{(1+$index).&ordinal-digit} super-Poulet number == " ~ @super-poulet[$index].,
}</lang>
- Output:
First 20 super-Poulet numbers: (341 1387 2047 2701 3277 4033 4369 4681 5461 7957 8321 10261 13747 14491 15709 18721 19951 23377 31417 31609) Index and value of first super-Poulet greater than one million: 109th super-Poulet number == 1,016,801 Index and value of first super-Poulet greater than ten million: 317th super-Poulet number == 10,031,653