A219254 Number of ways to express 2n+1 as p+4q with p, q primes.

0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 2, 2, 2, 3, 2, 2, 2, 2, 4, 4, 1, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 5, 0, 5, 7, 3, 3, 6, 3, 5, 3, 5, 4, 6, 2, 3, 6, 2, 5, 6, 3, 5, 5, 4, 6, 6, 3, 5, 7, 3, 4, 8, 3, 5, 5, 3, 4, 7, 3, 6, 6, 5, 5, 8, 4, 3, 8, 4, 5, 8, 1

Offset

0,8

Comments

This is related to the conjecture given in A219252.

a(38) = 0 because A219252(38) = 0.

Links

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

Example

a(15) = 4 because 31 = 23 + 4*2 = 19 + 4*3 = 11 + 4*5 = 3 + 4*7 with 4 decompositions.

Mathematica

a[n_] := (ways = 0; Do[p = 2k + 1; q = (n-k)/2; If[PrimeQ[p] && PrimeQ[q], ways++], {k, 1, n}]; ways); Table[a[n], {n, 0, 91}]

Crossrefs

Cf. A046927, A219252.

Sequence in context: A257977 A070966 A338669 * A072504 A072499 A060272

Adjacent sequences: A219251 A219252 A219253 * A219255 A219256 A219257

Keyword

nonn

Author

Michel Lagneau, Apr 11 2013

Extensions

Name corrected by Zak Seidov, Apr 14 2013

Status

approved