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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

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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]]