A329151 Primes p such that (3*p+q)/2 and (p+3*q)/2 are prime, where q is the next prime after p.

5, 29, 47, 139, 293, 557, 607, 647, 659, 709, 773, 809, 811, 863, 1117, 1171, 1187, 1801, 2129, 2467, 2477, 2549, 2917, 3023, 3229, 3329, 3389, 3469, 3593, 3617, 3833, 4261, 4363, 5791, 5849, 6269, 6781, 6949, 7069, 7703, 8273, 9397, 9973, 10141, 10343, 10369, 10529, 10657, 11059, 11329, 13063

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 25 2020

Keywords

• nonn

Comments

Intersection with A001359 is A069142.

Examples

			a(3)=47 is a term because it is prime, the next prime is 53, and (3*47+53)/2 = 97 and (47+3*53)/2 = 103 are both prime.
		

Links

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

Crossrefs

Cf. A001359, A069142.

Programs

Maple

Primes:= [seq(ithprime(i),i=1..10000)]:
Res:= NULL:
for i from 2 to nops(Primes)-1 do
   p:= Primes[i]; q:= Primes[i+1]; c:= (p+q)/2;
   if isprime(p+c) and isprime(q+c) then
     Res:= Res, p
   fi
od:
Res;