A227083 -id:A227083 - cp's OEIS frontend

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

Zhi-Wei Sun, Jul 02 2013

nonn

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.

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

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.

Cf. A000290, A008407, A227083.

cp's OEIS Frontend

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

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