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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, 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 (list; graph; refs; listen; history; text; internal format)
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 A023671

Adjacent sequences:  A227153 A227154 A227155 * A227157 A227158 A227159

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jul 02 2013

STATUS

approved

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Last modified December 18 15:01 EST 2014. Contains 252161 sequences.