A227156 Number of ways to write n as a sum of a square and half of a term of the sequence A008407

1, 1, 1, 2, 2, 1, 2, 2, 1, 3, 1, 2, 2, 2, 2, 2, 4, 1, 4, 2, 1, 4, 0, 3, 4, 3, 1, 3, 4, 2, 3, 2, 3, 4, 2, 1, 4, 2, 4, 4, 3, 4, 2, 4, 1, 5, 2, 1, 5, 3, 5, 2, 2, 4, 3, 3, 3, 3, 3, 3, 4, 1, 3, 5, 4, 4, 4, 2, 4, 4, 3, 4, 3, 6, 1, 3, 5, 2, 6, 4, 3, 7, 2, 4, 6, 2, 3, 5, 5, 2, 4, 4, 4, 6, 4, 3, 5, 3, 5, 3

Offset

1,4

Comments

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.

Links

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.

Example

a(195) = 1 since 195 = 0^2 + A008407(23)/2.
a(378) = 1 since 378 = 8^2 + A008407(110)/2.

Crossrefs

Cf. A000290, A008407, A227083.

Sequence in context: A247349 A069163 A025260 * A123369 A178306 A309363

Adjacent sequences: A227153 A227154 A227155 * A227157 A227158 A227159

Keyword

nonn

Author

Zhi-Wei Sun, Jul 02 2013

Status

approved