Consecutive primes with ascending or descending differences: Difference between revisions
Consecutive primes with ascending or descending differences (view source)
Revision as of 08:35, 16 November 2021
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λ> task (>) 1000000
[322171,322193,322213,322229,322237,322243,322247,322249]</pre>
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
This entry assumes the availability of `is_prime`, for which a suitable definition can be found at
[[Erd%C5%91s-primes#jq]].
'''Preliminaries'''
<lang jq># For streams of strings or of arrays or of numbers:
def add(s): reduce s as $x (null; .+$x);
# Primes less than . // infinite
def primes:
(. // infinite) as $n
| if $n < 3 then empty
else 2, (range(3; $n) | select(is_prime))
end;
</lang>
'''The Task'''
<lang jq># Input: null or limit+1
# Output: informative strings
def longestSequences:
[primes] as $primes
| def longestSeq(direction):
{ pd: 0,
longSeqs: [[2]],
currSeq: [2] }
| reduce range( 1; $primes|length) as $i (.;
($primes[$i] - $primes[$i-1]) as $d
| if (direction == "ascending" and $d <= .pd) or (direction == "descending" and $d >= .pd)
then if (.currSeq|length) > (.longSeqs[0]|length)
then .longSeqs = [.currSeq]
else if (.currSeq|length) == (.longSeqs[0]|length)
then .longSeqs = .longSeqs + [.currSeq]
else .
end
end
| .currSeq = [$primes[$i-1], $primes[$i]]
else .currSeq = .currSeq + [$primes[$i]]
end
| .pd = $d
)
| if (.currSeq|length) > (.longSeqs[0]|length)
then .longSeqs = [.currSeq]
else if (.currSeq|length) == (.longSeqs[0]|length)
then .longSeqs = .longSeqs + [.currSeq]
else .
end
end
| "Longest run(s) of primes with \(direction) differences is \(.longSeqs[0]|length):",
(.longSeqs[] as $ls
| add( range(1; $ls|length) | [$ls[.] - $ls[.-1]]) as $diffs
| add( range(0; $ls|length-1) | "\($ls[.]) (\($diffs[.])) ") + "\($ls[-1])" );
longestSeq("ascending"), "", longestSeq("descending");
"For primes < 1 million:",
( 1E6 | longestSequences )</lang>
{{out}}
<pre>
For primes < 1 million:
Longest run(s) of primes with ascending differences is 8:
128981 (2) 128983 (4) 128987 (6) 128993 (8) 129001 (10) 129011 (12) 129023 (14) 129037
402581 (2) 402583 (4) 402587 (6) 402593 (8) 402601 (12) 402613 (18) 402631 (60) 402691
665111 (2) 665113 (4) 665117 (6) 665123 (8) 665131 (10) 665141 (12) 665153 (24) 665177
Longest run(s) of primes with descending differences is 8:
322171 (22) 322193 (20) 322213 (16) 322229 (8) 322237 (6) 322243 (4) 322247 (2) 322249
752207 (44) 752251 (12) 752263 (10) 752273 (8) 752281 (6) 752287 (4) 752291 (2) 752293
</pre>
=={{header|Julia}}==
| |||