%I #18 Sep 08 2022 08:45:33
%S 37,67,277,1297,1307,1613,2099,2333,3533,3571,5507,8849,9029,10061,
%T 10289,13697,14621,17203,18013,18127,22613,23053,28559,30859,37357,
%U 39233,47407,47681,49537,49999,53239,55639,58379,67421,68863,70937
%N Primes p such that the left prime neighbors p1, p2 of p as well as the right prime neighbors q1, q2 of p form twin prime pairs and the sum p1 + p2 + p + q1 + q2 is also prime.
%H Harvey P. Dale, <a href="/A138396/b138396.txt">Table of n, a(n) for n = 1..1000</a>
%e The left prime neighbors 29, 31 of prime 37 and the right prime neighbors 41, 43 of 37 form twin prime pairs, and the sum 29+31+37+41+43 = 181 is prime. Hence 37 is in the sequence.
%t Select[Partition[Prime[Range[8000]],5,1],#[[2]]-#[[1]]==#[[5]]-#[[4]] == 2 && PrimeQ[Total[#]]&][[All,3]] (* _Harvey P. Dale_, Oct 01 2017 *)
%o (Magma) P:= PrimesUpTo(71000); [ n: k in [3..#P-2] | p2-p1 eq 2 and q2-q1 eq 2 and IsPrime(p1+p2+n+q1+q2) where p1 is P[k-2] where p2 is P[k-1] where n is P[k] where q1 is P[k+1] where q2 is P[k+2] ]; // _Klaus Brockhaus_, Dec 04 2009
%Y Cf. A001097 (twin primes).
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 08 2008
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008
%E Edited by _Klaus Brockhaus_, Dec 04 2009
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