A225518 Number of ways to express 2n+1 as p + 8*q, with p and q primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 3, 0, 1, 3, 1, 2, 3, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 1, 3, 2, 3, 1, 2, 3, 3, 2, 4, 2, 2, 2, 4, 2, 3, 3, 2, 4, 3, 2, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 2, 5, 3, 2, 4, 5, 3, 4, 2, 4, 5, 4, 2, 4, 3

Offset

0,14

Comments

This is related to the conjecture given in A223174 and A223175.

For n > 8, a(12) = a(24) = 0 because A223174(12)= A223174(24)= 0.

Links

Michel Lagneau, Table of n, a(n) for n = 0..10000

Example

a(14) = 2 because 29 = 5+8*3 = 13+8*2 with 2 decompositions.
a(23) = 3 because 47 = 7+8*5 = 23+8*3 = 31+8*2 with 3 decompositions.

Mathematica

a[n_] := (ways = 0; Do[p = 2k + 1; q = (n-k)/4; If[PrimeQ[p] && PrimeQ[q], ways++], {k, 1, n}]; ways); Table[a[n], {n, 0, 90}]

Crossrefs

Cf. A219254, A223174, A223175.

Sequence in context: A330348 A117229 A264119 * A269972 A202205 A336123

Adjacent sequences: A225515 A225516 A225517 * A225519 A225520 A225521

Keyword

nonn

Author

Michel Lagneau, May 09 2013

Status

approved