A124662 Primes prime(n) such that there exists a 0 < k < n-1 such that prime(n+k) + prime(n-k) = 2*prime(n).

5, 11, 13, 17, 29, 31, 37, 41, 53, 59, 61, 67, 71, 83, 89, 97, 101, 103, 107, 127, 131, 137, 139, 151, 157, 167, 173, 179, 181, 191, 193, 197, 211, 233, 251, 257, 263, 277, 307, 311, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421

Offset: 1

Author

Artur Jasinski, Dec 23 2006

Keywords

• nonn

Comments

prime(11+3) + prime(11-3) = 2*prime(11); therefore prime(11) = 31 is in the sequence.

Programs

Mathematica

a = {}; For[k = 3, k < 100, k++, For[n = 1, n < k - 1, n++, If[(Prime[k + n] + Prime[k - n])/2 == Prime[k], AppendTo[a, Prime[k]]]]]; Union[a, a]

Extensions

Edited, corrected and extended by Stefan Steinerberger, Jul 31 2007