A336300 Primes p such that there exists k with p < k < q such that p+k and q+k are prime, where q is the next prime after p.

5, 23, 29, 31, 47, 53, 73, 83, 113, 131, 139, 151, 173, 199, 211, 251, 293, 317, 359, 373, 467, 491, 509, 523, 541, 557, 593, 607, 647, 659, 683, 709, 719, 761, 773, 797, 809, 811, 863, 911, 991, 997, 1063, 1069, 1103, 1117, 1163, 1171, 1187, 1201, 1231, 1259, 1307, 1327, 1409, 1439, 1459, 1499

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 22 2020

Keywords

• nonn

Comments

There may be more than one such k: thus for a(17) = 293, k = 294, 300, and 306 all work.

Examples

			a(4)=31 is included because 31 is prime, the next prime after 31 is 37, and with k=36 we have 31+36=67 and 37+36=73 both prime.
		

Links

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

Crossrefs

Includes A069142.

Programs

Maple

P:= [seq(ithprime(i),i=2..1000)]:
R:= NULL:
for i from 1 to nops(P)-1 do
  for k from ceil(P[i]/2) to floor(P[i+1]/2) do
    if isprime(P[i]+2*k) and isprime(P[i+1]+2*k) then
      R:= R, P[i]; break
    fi
  od;
od:
R;