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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

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

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[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

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

Zhi-Wei Sun, Oct 12 2013

STATUS

approved

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Last modified August 8 09:40 EDT 2022. Contains 356009 sequences. (Running on oeis4.)