A236831 - OEIS

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A236831

Number of ordered ways to write n = p + q with q > 0 such that p, p + 2 and p + prime(q) + 1 are all prime.

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

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OFFSET

1,9

COMMENTS

Conjecture: a(n) > 0 for all n > 13.

LINKS

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

Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

EXAMPLE

a(12) = 1 since 12 = 5 + 7 with 5, 5 + 2 = 7 and 5 + prime(7) + 1 = 5 + 17 + 1 = 23 all prime.

a(85) = 1 since 85 = 29 + 56 with 29, 29 + 2 = 31 and 29 + prime(56) + 1 = 29 + 263 + 1 = 293 all prime.

MATHEMATICA