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 A138396 Primes n such that the left prime neighbors p1, p2 of n as well as the right prime neighbors q1, q2 of n form twin prime pairs and the sum p1+p2+n+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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Might be called penta-primes. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 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 a={}; Do[p0=Prime[n]; a1=Prime[n-2]; a2=Prime[n-1]; b1=Prime[n+1]; b2=Prime[n+2]; sp=a1+a2+p0+b1+b2; If[PrimeQ[sp]&&a2-a1==2&&b2-b1==2, AppendTo[a, p0]], {n, 3, 10^3}]; a Select[Partition[Prime[Range], 5, 1], #[]-#[]==#[]-#[] == 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 * A155087 A171807 A178399 Adjacent sequences:  A138393 A138394 A138395 * A138397 A138398 A138399 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, May 08 2008 EXTENSIONS More terms from Vladimir Joseph Stephan Orlovsky, Dec 17 2008 Edited by Klaus Brockhaus, Dec 04 2009 STATUS approved

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)