

A230351


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


8



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

1,5


COMMENTS

Conjecture: a(n) > 0 for all n > 3.
We have verified this for n up to 2*10^7.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588.


EXAMPLE

a(7) = 1 since 7 = 3 + 4 with 3, 2*3^2  1 = 17, 2*4^2  1 = 31 all prime.
a(40) = 1 since 40 = 2 + 38, and 2, 2*2^2  1 = 7 , 2*38^2  1 = 2887 are all prime.
a(68) = 1 since 68 = 43 + 25, and all the three numbers 43, 2*43^2  1 = 3697 and 2*25^2  1 = 1249 are prime.


MATHEMATICA

a[n_]:=Sum[If[PrimeQ[2Prime[i]^21]&&PrimeQ[2(nPrime[i])^21], 1, 0], {i, 1, PrimePi[n1]}]
Table[a[n], {n, 1, 100}]


CROSSREFS

Cf. A000040, A066049, A106483, A219864, A230252, A230254, A230261.
Sequence in context: A268507 A272351 A243612 * A102481 A231201 A295515
Adjacent sequences: A230348 A230349 A230350 * A230352 A230353 A230354


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Oct 16 2013


STATUS

approved



