A341215 Primes p such that 2*p+3*q and 3*p+2*q are prime, where q is the next prime after p.

5, 7, 11, 19, 29, 31, 37, 43, 53, 113, 127, 163, 173, 199, 257, 271, 317, 353, 397, 439, 457, 461, 557, 599, 659, 757, 809, 991, 997, 1019, 1069, 1129, 1289, 1327, 1439, 1447, 1549, 1621, 1733, 1747, 1759, 1831, 1913, 2027, 2113, 2141, 2153, 2309, 2339, 2357, 2383, 2423, 2473, 2663, 2741, 2801

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 06 2021

Keywords

• nonn

Examples

			a(3) = 11 is a term because the next prime is 13 and 2*11+3*13 = 61 and 3*11+2*13 = 59 are prime.
		

Links

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

Crossrefs

Contains A174922.

Programs

Maple

R:=  NULL: count:= 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(p);
  if isprime(2*p+3*q) and isprime(3*p+2*q) then
    count:= count+1; R:= R, p
  fi
od:
R;

Mathematica

Select[Partition[Prime[Range[500]],2,1],AllTrue[{2#[[1]]+3#[[2]],3#[[1]]+2#[[2]]},PrimeQ]&][[;;,1]] (* Harvey P. Dale, Jun 11 2025 *)

PARI

isok(p) = isprime(p) && (q=nextprime(p+1)) && isprime(2*p+3*q) && isprime(3*p+2*q); \\ Michel Marcus, Feb 07 2021