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A235613 Number of ways to write n = k + m (0 < k <= m) with k and m terms of A235592. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A136510 A080071 A202472 * A322418 A019569 A003434

Adjacent sequences:  A235610 A235611 A235612 * A235614 A235615 A235616

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 12 2014

STATUS

approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)