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%I #17 Jul 28 2022 03:51:24
%S 2,4,10,5996,8894,11204,14290,23110,30866,37594,43054,64390,74554,
%T 83464,93460,109456,111940,132304,151904,184706,238850,262630,265990,
%U 277630,300206,315410,352600,355450,376190,404954,415180,462830,483494,512354,512704,566296
%N Numbers k such that k^2 + {1,3,7,13} are prime.
%C Conjecture: the sequence is infinite.
%e 2^2 + {1,3,7,13} = {5,7,11,17} all prime.
%e 4^2 + {1,3,7,13} = {17,19,23,29} all prime.
%p q:= k-> andmap(j-> isprime(k^2+j), [1,3,7,13]):
%p select(q, [$0..1000000])[]; # _Alois P. Heinz_, Jul 27 2022
%t Select[Range[500000], AllTrue[#^2 + {1,3,7,13}, PrimeQ] &] (* _Amiram Eldar_, Jul 27 2022 *)
%o (Python)
%o from sympy import isprime
%o def ok(n): return all(isprime(n*n+i) for i in {1,3,7,13})
%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Jul 27 2022
%Y Intersection of A005574, A049422, A114270, A113536.
%Y Subsequence of A182238.
%K nonn
%O 1,1
%A _Michel Lagneau_, Jul 27 2022
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