A355485 Primes p such that neither g-1 nor g+1 is prime, where g is the gap from p to the next prime.

1327, 2477, 3137, 5531, 8467, 9973, 11213, 11743, 12011, 12163, 12347, 14897, 16007, 16493, 16703, 17257, 19087, 20297, 20443, 21433, 24443, 26267, 26513, 29033, 29501, 29683, 31193, 31907, 32653, 32843, 34549, 34781, 35543, 35771, 36161, 36497, 36947, 37061, 37747, 38993, 39581, 40361, 40433

Offset: 1

Author

J. M. Bergot and Robert Israel, Jul 04 2022

Keywords

• nonn

Comments

Primes prime(i) where A001223(i) is in A061673.

Examples

			a(3) = 3137 is a term because 3137 is prime, the next prime is 3163 = 3137+26, and neither 26-1 = 25 nor 26+1 = 27 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001223, A061673.

Programs

Maple

q:= 2:
count:= 0:
R:= NULL:
while count < 100 do
  p:= q;
  q:= nextprime(q);
  g:= q-p;
  if not(isprime(g-1) or isprime(g+1)) then
     count:= count+1;
     R:= R, p
  fi
od:
R;

PARI

isok(p) = if (isprime(p), my(g=nextprime(p+1)-p); !isprime(g-1) && !isprime(g+1)); \\ Michel Marcus, Jul 05 2022