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%I #29 Mar 03 2024 10:15:10
%S 66,96,1446,2706,7206,9336,11826,19416,21516,28656,42696,52176,71706,
%T 79146,81546,88806,126486,136986,140676,151896,159786,167436,188856,
%U 222786,223836,245976,266676,272346,284736,330426,340926,349926,375246,375996,389526,395106
%N Numbers k such that k - 13, k + 1, k + 5, k + 7, and k + 13 are all prime.
%C Consider 4 distinct numbers a, b, c, d such that all 5 numbers a+b+c+d, -a+b+c+d, a-b+c+d, a+b-c+d and a+b+c-d are positive/negative primes. The sequence give values of d for fixed values a=3, b=4, c=6.
%C Apparently a=3, b=4, c=6 is the least possible set.
%H Zak Seidov, <a href="/A281937/b281937.txt">Table of n, a(n) for n = 1..1000</a>
%t Reap[Do[If[PrimeQ[a + b - c + d] && PrimeQ[a - b + c + d] && PrimeQ[-a + b + c + d] && PrimeQ[a + b + c - d] && PrimeQ[a + b + c + d], Sow[d]], {a, 3, 3}, {b, 4,4}, {c, 6, 6}, {d, 1 + c, 100000}]][[2, 1]]
%t fQ[n_] := Times @@ Boole@ PrimeQ[{n +13, n +7, n +5, n +1, n -13}] == 1; Select[6 + 30*Range[2, 13100], fQ] (* _Robert G. Wilson v_, Feb 03 2017 *)
%o (PARI) is(n)=isprime(n-13) && isprime(n+1) && isprime(n+5) && isprime(n+7) && isprime(n+13) \\ _Charles R Greathouse IV_, Feb 06 2017
%K nonn
%O 1,1
%A _Zak Seidov_, Feb 02 2017
%E New NAME from _Charles R Greathouse IV_, Feb 06 2017