A339414 Primes p such that (p+q)/4 is prime, where q is the next prime after p.

3, 5, 23, 31, 83, 131, 251, 271, 331, 383, 443, 563, 971, 1123, 1223, 1231, 1283, 1291, 1543, 2063, 2371, 2383, 2551, 2851, 2903, 2963, 3083, 3323, 3691, 3889, 4051, 4283, 4591, 4733, 4831, 4871, 4951, 5003, 5209, 5351, 5683, 5711, 5851, 6229, 6271, 6323, 6491, 6863, 6911, 7393, 7451, 7583, 7643

Offset: 1

Author

Robert Israel, Dec 03 2020

Keywords

• nonn

Comments

After the initial 2 terms, a(n)=2*A118134(n)-3. - Hugo Pfoertner, Dec 03 2020

Examples

			a(5)=83 is in the sequence because it is prime, the next prime is 89, and (83+89)/4 = 43 is prime.
		

Links

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

Crossrefs

Subset of A098058.

Cf. A118134.

Programs

Maple

P:= select(isprime, [seq(i,i=3..10000,2)]):
R:= (P[1..-2]+P[2..-1])/4:
P[select(i-> R[i]::integer and isprime(R[i]), [$1..nops(R)])];

PARI

isok(p) = isprime(p) && iferr(isprime((p+nextprime(p+1))/4),E,0); \\ Michel Marcus, Dec 04 2020