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%I #6 Apr 01 2021 15:12:56
%S 11459317,18726137,73718633,181975727,361471043,374195537,419533753,
%T 420522673,428739323,429198703,456975157,483576523,544795393,
%U 653578573,682118777,703313623,753422317,764967257,797492477,960985037,1059913073
%N Primes p such that p-6^4, p-6^3, p-6^2, p-6, p, p+6, p+6^2, p+6^3 and p+6^4 are primes.
%C Subsequence of A006489, A141279 and A141280. Each term is congruent to 1 or 10 mod 11 so for no prime p can this pattern be extended also to include primes p-6^5 and p+6^5 (one of them is divisible by 11). See A070392 for residues mod 11 of powers of 6. As each term of A006489 greater than 11 is congruent to 3 or 7 mod 10, combining results gives that a(n) is congruent to 23, 43, 67, or 87 mod 110.
%H Rick L. Shepherd, <a href="/A141281/b141281.txt">Table of n, a(n) for n = 1..55</a>
%t Select[Prime[Range[53734400]],AllTrue[#+{1296,216,36,6,-6,-36,-216,-1296},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 01 2021 *)
%Y Cf. A006489, A141279, A141280, A141282, A070392.
%K nonn
%O 1,1
%A _Rick L. Shepherd_, Jun 22 2008