A335139 a(n) = (prime(n + 1) +- k) / 2 where k is the smallest possible odd number such that a(n) is prime and a(n + 1) >= a(n).

2, 3, 3, 5, 7, 7, 11, 11, 13, 17, 19, 19, 23, 23, 29, 29, 31, 31, 37, 37, 41, 41, 43, 47, 53, 53, 53, 53, 59, 61, 67, 67, 71, 73, 73, 79, 83, 83, 89, 89, 89, 97, 97, 97, 101, 107, 113, 113, 113, 113, 113, 127, 127, 127, 131, 137, 137, 139, 139, 139, 149

Offset: 1

Author

Dimitris Valianatos, May 24 2020

Keywords

• nonn

Comments

The sequence of k's begins {1, 1, -1, -1, 1, -3, 3, -1, -3, 3, 1, -3, 3, -1, ...}. I conjecture that the partial sums of the k's sequence change sign infinitely often and that their absolute value is less than the square root of n.

Crossrefs

Cf. A000040.

Programs

PARI

forprime(n = 3, 300, forstep(j = 1, 999, 2, a = (n + j)/2; b =(n - j)/2; if(isprime(a), print1(a", "); break); if(isprime(b), print1(b", "); break)))