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

Author

Zhi-Wei Sun, Jan 12 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A235592, A235614.

Programs

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}]