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

1,1

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.

Links

Table of n, a(n) for n=1..61.

Prog

(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)))

Crossrefs

Cf. A000040.

Sequence in context: A343224 A047844 A081217 * A320036 A053271 A035360

Adjacent sequences: A335136 A335137 A335138 * A335140 A335141 A335142

Keyword

nonn

Author

Dimitris Valianatos, May 24 2020

Status

approved