OFFSET
1,20
COMMENTS
Conjecture: a(n) > 0 for all n > 17.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..3000
Zhi-Wei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588.
EXAMPLE
MATHEMATICA
RQ[n_]:=n>5&&PrimeQ[3n-4]&&PrimeQ[3n-10]&&PrimeQ[3n-14]
SQ[n_]:=PrimeQ[n]&&RQ[n]
a[n_]:=Sum[If[RQ[Prime[i]]&&RQ[Prime[j]]&&RQ[Prime[k]]&&SQ[2n-Prime[i]-Prime[j]-Prime[k]], 1, 0],
{i, 1, PrimePi[n/2]}, {j, i, PrimePi[(2n-Prime[i])/3]}, {k, j, PrimePi[(2n-Prime[i]-Prime[j])/2]}]
Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 12 2013
STATUS
approved