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

1,1

Comments

Intersection with A001359 is A069142.

Links

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

Example

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.

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;

Crossrefs

Cf. A001359, A069142.

Sequence in context: A192090 A268673 A146829 * A201712 A271923 A224499

Adjacent sequences: A329148 A329149 A329150 * A329152 A329153 A329154

Keyword

nonn

Author

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

Status

approved