

A230224


Number of ways to write 2*n = p + q + r + s with p <= q <= r <= s such that p, q, r, s are primes in A230223.


5



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 4, 1, 3, 3, 3, 4, 4, 3, 5, 4, 5, 3, 6, 4, 6, 5, 5, 5, 7, 5, 9, 4, 6, 6, 8, 6, 9, 5, 7, 7, 10, 6, 8, 7, 8, 7, 9, 5, 10, 7, 11, 7, 7, 7, 11, 7, 10, 6, 10, 6, 13, 7, 9, 7, 11, 9, 11, 7, 9, 6, 14, 8, 12, 6, 13, 11, 12, 11, 13, 10, 16, 9, 14, 7, 14
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,20


COMMENTS

Conjecture: a(n) > 0 for all n > 17.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..3000
ZhiWei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588.


EXAMPLE

a(21) = 1 since 2*21 = 7 + 7 + 11 + 17, and 7, 11, 17 are primes in A230223.
a(27) = 1 since 2*27 = 7 + 11 + 17 + 19, and 7, 11, 17, 19 are primes in A230223.


MATHEMATICA

RQ[n_]:=n>5&&PrimeQ[3n4]&&PrimeQ[3n10]&&PrimeQ[3n14]
SQ[n_]:=PrimeQ[n]&&RQ[n]
a[n_]:=Sum[If[RQ[Prime[i]]&&RQ[Prime[j]]&&RQ[Prime[k]]&&SQ[2nPrime[i]Prime[j]Prime[k]], 1, 0],
{i, 1, PrimePi[n/2]}, {j, i, PrimePi[(2nPrime[i])/3]}, {k, j, PrimePi[(2nPrime[i]Prime[j])/2]}]
Table[a[n], {n, 1, 100}]


CROSSREFS

Cf. A002375, A068307, A230223, A230140, A230141, A230219.
Sequence in context: A049099 A181776 A243036 * A206941 A327790 A143179
Adjacent sequences: A230221 A230222 A230223 * A230225 A230226 A230227


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Oct 12 2013


STATUS

approved



