A306627 Primes of the form (p + prime(p))/2 with prime p.

43, 53, 79, 97, 199, 257, 347, 1103, 1187, 1303, 1367, 1753, 2029, 2351, 2593, 2647, 3181, 3253, 4663, 4787, 4903, 4919, 5573, 6091, 7079, 7331, 7369, 7457, 8101, 8527, 8543, 10159, 11549, 12647, 13151, 14699, 15031, 15559, 15679, 15881, 15889, 16661, 17099, 17881, 18251, 18959, 19219, 20399, 20431

Offset: 1

Author

Zak Seidov, Mar 01 2019

Keywords

• nonn

Comments

Indices k of p's are 8, 9, 11, 12, 19, 23, 28, 62, 64, 68, 71, 85, 95, 104, 114, 115, 131, 134, 175, 178, 181, 182, 200, 216, 240, 246, 247, 250, 266, 276, 277, 316, 346, 372, 382.

And some of k's themselves are prime: 11, 19, 23, 71, 131, 181, 277, 421, 541, 601, 673, 751, 881, 937. See link to Fernandez.

Examples

			43 = (p + prime(p))/2 for p = 19 (prime),
53 = (p + prime(p))/2 for p = 23 (prime).
		

Links

• Neil Fernandez, An order of primeness.

Crossrefs

Cf. A014688 (n-th prime + n).

Programs

PARI

lista(nn) = forprime(p=3,nn,k=(prime(p)+p)/2;if(isprime(k),print1(k, ", "))) \\ Jinyuan Wang, Mar 01 2019