

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
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OFFSET

1,1


COMMENTS

Might be called pentaprimes.


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[n2]; a2=Prime[n1]; b1=Prime[n+1]; b2=Prime[n+2]; sp=a1+a2+p0+b1+b2; If[PrimeQ[sp]&&a2a1==2&&b2b1==2, AppendTo[a, p0]], {n, 3, 10^3}]; a
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..#P2]  p2p1 eq 2 and q2q1 eq 2 and IsPrime(p1+p2+n+q1+q2) where p1 is P[k2] where p2 is P[k1] 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



