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A138396
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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.
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1
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37, 67, 277, 1297, 1307, 1613, 2099, 2333, 3533, 3571, 5507, 8849, 9029, 10061, 10289, 13697, 14621, 17203, 18013, 18127, 22613, 23053, 28559, 30859, 37357, 39233, 47407, 47681, 49537, 49999, 53239, 55639, 58379, 67421, 68863, 70937
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OFFSET
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1,1
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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EXAMPLE
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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.
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MATHEMATICA
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Select[Partition[Prime[Range[8000]], 5, 1], #[[2]]-#[[1]]==#[[5]]-#[[4]] == 2 && PrimeQ[Total[#]]&][[All, 3]] (* Harvey P. Dale, Oct 01 2017 *)
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PROG
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(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
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CROSSREFS
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Cf. A001097 (twin primes).
Sequence in context: A063461 A105462 A119381 * A335484 A155087 A171807
Adjacent sequences: A138393 A138394 A138395 * A138397 A138398 A138399
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KEYWORD
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nonn
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, May 08 2008
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EXTENSIONS
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More terms from Vladimir Joseph Stephan Orlovsky, Dec 17 2008
Edited by Klaus Brockhaus, Dec 04 2009
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STATUS
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approved
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