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A138396
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.
1
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
OFFSET
1,1
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Partition[Prime[Range[8000]], 5, 1], #[[2]]-#[[1]]==#[[5]]-#[[4]] == 2 && PrimeQ[Total[#]]&][[All, 3]] (* Harvey P. Dale, Oct 01 2017 *)
PROG
(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
CROSSREFS
Cf. A001097 (twin primes).
Sequence in context: A063461 A105462 A119381 * A335484 A155087 A171807
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Dec 17 2008
Edited by Klaus Brockhaus, Dec 04 2009
STATUS
approved