A024684 Number of ways prime(n) is a sum of three distinct primes.

0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 6, 9, 11, 13, 13, 15, 18, 17, 19, 25, 26, 28, 32, 31, 37, 32, 39, 44, 51, 54, 48, 60, 55, 62, 64, 73, 80, 79, 74, 89, 84, 92, 86, 92, 107, 119, 105, 118, 122, 117, 135, 143, 146, 147, 141, 149, 159, 157, 176, 175, 190, 180

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			a(9) = 2 because prime(9) = 23 and 23 = 3 + 7 + 13 = 5 + 7 + 11.
		

Links

• Zak Seidov and T. D. Noe, Table of n, a(n) for n = 1..10000 (first 2000 terms from Zak Seidov)
• Wikipedia, Goldbach's weak conjecture

Crossrefs

Cf. A002372, A002375, A224534.

Programs

Mathematica

last = 313; pp = PrimePi[last]; t = Select[Sort[Tally[Select[Total /@ Subsets[Prime[Range[2, pp]], {3}], PrimeQ]]], #[[1]] <= last &]; Join[{0, 0, 0, 0, 0, 0, 0}, Transpose[t][[2]]] (* T. D. Noe, Apr 15 2013 *)

Formula

a(n) = A125688(prime(n)). - R. J. Mathar, Jun 09 2014