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A163182
Primes p such that neither 4p+3 nor 4p-3 are prime.
1
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Jul 25 2009, Jul 27 2009
STATUS
approved