A235613 Number of ways to write n = k + m (0 < k <= m) with k and m terms of A235592.

0, 0, 0, 1, 1, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 4, 3, 5, 6, 5, 4, 4, 3, 4, 6, 5, 4, 5, 4, 4, 5, 4, 4, 6, 5, 8, 6, 6, 5, 5, 6, 6, 8, 6, 6, 6, 4, 7, 6, 5, 7, 9, 6, 6, 8, 5, 4, 7, 9, 7, 8, 6, 6, 7, 3, 5, 7, 9, 8, 9, 9, 6, 6, 5, 6, 7, 6, 8, 5, 4, 4, 4, 4, 8, 10, 10, 10, 7, 6, 6, 8, 7, 6, 10, 6, 6

Offset

1,6

Comments

Conjecture: a(n) > 0 for all n > 3.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(4) = 1 since 4 = 2 + 2 with 2*(2+1) - prime(2) = 3 prime.
a(5) = 1 since 5 = 2 + 3 with 2*(2+1) - prime(2) = 3 and 3*(3+1) - prime(3) = 7 both prime.

Mathematica

p[n_]:=PrimeQ[n(n+1)-Prime[n]]
a[n_]:=Sum[If[p[k]&&p[n-k], 1, 0], {k, 1, n/2}]
Table[a[n], {n, 1, 100}]

Crossrefs

Cf. A000040, A235592, A235614.

Sequence in context: A080071 A340862 A202472 * A322418 A019569 A003434

Adjacent sequences: A235610 A235611 A235612 * A235614 A235615 A235616

Keyword

nonn

Author

Zhi-Wei Sun, Jan 12 2014

Status

approved