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

1,1

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.

Links

Table of n, a(n) for n=1..49.

N. Fernandez, An order of primeness

Example

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

Prog

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

Crossrefs

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

Sequence in context: A095744 A156252 A364689 * A342771 A174818 A280388

Adjacent sequences: A306624 A306625 A306626 * A306628 A306629 A306630

Keyword

nonn

Author

Zak Seidov, Mar 01 2019

Status

approved