A339775 Primes p such that (p+nextprime(p))/6 is prime and 6*p is the sum of two consecutive primes.

5, 7, 13, 37, 127, 389, 719, 937, 3089, 7669, 9199, 12211, 17099, 17519, 18919, 19259, 19273, 19853, 20063, 21379, 22453, 22643, 23059, 23143, 23173, 23753, 24113, 24329, 25339, 25873, 31387, 31667, 32803, 33203, 34057, 34183, 36629, 37253, 37831, 37967, 38557, 39293, 40429, 41039, 42743, 48163

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 16 2020

Keywords

• nonn

Examples

			a(3) = 13 is a term because 13 is prime, the next prime is 17, (13+17)/6 = 5 is prime, and 6*13 = 78 = 37 + 41 is the sum of consecutive primes.
		

Links

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

Crossrefs

Intersection of A163487 and A288632.

Programs

Maple

filter:= proc(p) local q;
  if not isprime(p) then return false fi;
  q:= prevprime(3*p);
  if q + nextprime(q) <> 6*p then return false fi;
  q:= (p+nextprime(p))/6;
  q::integer and isprime(q)
end proc:
select(filter, [seq(i,i=3..10^5,2)]);