

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.


6



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

ZhiWei 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

p[n_, m_]:=PrimeQ[m+2]&&PrimeQ[m+Prime[nm]+1]
a[n_]:=Sum[If[p[n, Prime[k]], 1, 0], {k, 1, PrimePi[n1]}]
Table[a[n], {n, 1, 100}]


CROSSREFS

Cf. A000040, A001359, A006512, A236531.
Sequence in context: A118832 A122807 A105700 * A030205 A159817 A079532
Adjacent sequences: A236828 A236829 A236830 * A236832 A236833 A236834


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Jan 31 2014


STATUS

approved



