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

Author

Vladimir Joseph Stephan Orlovsky, Jul 22 2009

Keywords

• nonn
• easy

Comments

Primes neither in A023213 nor in A157978.

Examples

			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.
		

Links

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

Crossrefs

Cf. A023213, A106015, A157978.

Programs

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 *)

PARI

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

Extensions

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