1,4

Conjecture: We have a(n) > 0 except for n = 23.

We also conjecture that any positive integer can be written as a sum of a triangular number and half of a term of A008407, and each integer n > 4 can be written as x + y (x>0, y>0) with x*y a term of A008407.

Zhi-Wei Sun, Table of n, a(n) for n = 1..1164

A. V. Sutherland, Narrow admissible k-tuples: bounds on H(k), 2013.

T. Tao, Bounded gaps between primes, PolyMath Wiki Project, 2013.

a(195) = 1 since 195 = 0^2 + A008407(23)/2.

a(378) = 1 since 378 = 8^2 + A008407(110)/2.

Cf. A000290, A008407, A227083.

Sequence in context: A247349 A069163 A025260 * A123369 A178306 A280153

Adjacent sequences: A227153 A227154 A227155 * A227157 A227158 A227159

nonn

Zhi-Wei Sun, Jul 02 2013

approved