A163182 Primes p such that neither 4p+3 nor 4p-3 are prime.

3, 13, 43, 53, 73, 83, 97, 127, 137, 139, 163, 167, 173, 197, 199, 211, 223, 251, 269, 277, 281, 293, 311, 317, 337, 347, 379, 383, 397, 409, 419, 421, 433, 443, 449, 463, 491, 503, 547, 557, 563, 593, 601, 607, 613, 617, 641, 643, 727, 733, 757, 787, 809

Offset

1,1

Comments

Primes neither in A023213 nor in A157978.

Links

Marius A. Burtea, Table of n, a(n) for n = 1..5673

Example

For p=3, 4*3+3=15 (not prime) and 4*3-3=9 (not prime), so the prime p=3 is in the sequence.
For p=7, 4*7+3=31 (prime), so the prime p=7 is not in the sequence.

Mathematica

lst={}; Do[p=Prime[n]; If[ !PrimeQ[2*p+(p-1)+(p-2)]&&!PrimeQ[2*p+(p+1)+(p+2)], AppendTo[lst, p]], {n, 3*5!}]; lst
Select[Prime[Range[150]], NoneTrue[4#+{3, -3}, PrimeQ]&] (* Harvey P. Dale, Aug 01 2022 *)

Prog

(PARI) isok(p) = isprime(p) && !isprime(4*p+3) && !isprime(4*p-3); \\ Michel Marcus, Oct 12 2018

Crossrefs

Cf. A023213, A106015, A157978.

Sequence in context: A074425 A041499 A093923 * A267455 A138249 A181604

Adjacent sequences: A163179 A163180 A163181 * A163183 A163184 A163185

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 22 2009

Extensions

Edited by R. J. Mathar, Jul 25 2009, Jul 27 2009

Status

approved