Ludic numbers: Difference between revisions
→{{header|jq}}
Line 2,035:
233, 235, 239
</pre>
=={{header|jq}}==
{{works with|jq}}
In this entry, for each task, we do not assume any prior calculation of how big the initial sieve must be.
That is, an adaptive approach is taken.
<lang jq># This method for sieving turns out to be the fastest in jq.
# Input: an array to be sieved.
# Output: if the array length is less then $n then empty, else the sieved array.
def sieve($n):
if length<$n then empty
else . as $in
| reduce range(0;length) as $i ([]; if $i % $n == 0 then . else . + [$in[$i]] end)
end;
# Generate a stream of ludic numbers based on sieving range(2; $nmax+1)
def ludic($nmax):
def l:
.[0] as $next
| $next, (sieve($next)|l);
1, ([range(2; $nmax+1)] | l);
# Output: an array of the first . ludic primes (including 1)
def first_ludic_primes:
. as $n
| def l:
. as $k
| [ludic(10*$k)] as $a
| if ($a|length) >= $n then $a[:$n]
else (10*$k) | l
end;
l;
# Output: an array of the ludic numbers less than .
def ludic_primes:
. as $n
| def l:
. as $k
| [ludic(10*$k)] as $a
| if $a[-1] >= $n then $a | map(select(. < $n))
else (10*$k) | l
end;
l;
# Output; a stream of triplets of ludic numbers, where each member of the triplet is less than .
def triplets:
ludic_primes as $primes
| $primes[] as $p
| $primes
| bsearch($p) as $i
| if $i >= 0
then $primes[$i+1:]
| select( bsearch($p+2) >= 0 and
bsearch($p+6) >= 0)
| [$p, $p+2, $p+6]
else empty
end;
"First 25 ludic primes:", (25|first_ludic_primes),
"\nThere are \(1000|ludic_primes|length) ludic numbers <= 1000",
( "The \n2000th to 2005th ludic primes are:",
(2005|first_ludic_primes)[2000:]),
( [250 | triplets]
| "\nThere are \(length) triplets less than 250:",
.[] )</lang>
{{out}}
<pre>
First 25 ludic primes:
[1,2,3,5,7,11,13,17,23,25,29,37,41,43,47,53,61,67,71,77,83,89,91,97,107]
There are 142 ludic numbers <= 1000
2000th to 2005th ludic primes:
[21481,21487,21493,21503,21511]
There are 8 triplets less than 250:
[1,3,7]
[5,7,11]
[11,13,17]
[23,25,29]
[41,43,47]
[173,175,179]
[221,223,227]
[233,235,239]
</pre>
=={{header|Julia}}==
| |||