A022902 Number of solutions to c(1)*prime(3)+...+c(n)*prime(n+2) = 2, where c(i) = +-1 for i>1, c(1) = 1.

0, 0, 0, 0, 0, 1, 0, 1, 0, 5, 0, 18, 0, 59, 0, 180, 0, 576, 0, 1993, 0, 6864, 0, 23804, 0, 83796, 0, 300913, 0, 1066508, 0, 3831226, 0, 13815422, 0, 50187328, 0, 183452325, 0, 674196751, 0, 2485443437, 0, 9232423194, 0, 34201130579, 0, 127197104929, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			a(10) counts these 5 solutions: {5, -7, -11, 13, -17, 19, -23, 29, 31, -37}, {5, -7, -11, 13, -17, 19, 23, -29, -31, 37}, {5, -7, 11, 13, -17, -19, -23, -29, 31, 37}, {5, 7, -11, -13, -17, 19, -23, 29, -31, 37}, {5, 7, -11, -13, 17, -19, -23, -29, 31, 37}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..500

Programs

Mathematica

{f, s} = {3, 2}; Table[t = Map[Prime[# + f - 1] &, Range[2, z]]; Count[Map[Apply[Plus, #] &, Map[t # &, Tuples[{-1, 1}, Length[t]]]], s - Prime[f]], {z, 22}]
(* A022902, a(n) = number of solutions of "sum = s" using Prime(f) to Prime(f+n-1) *)
n = 10; t = Map[Prime[# + f - 1] &, Range[n]]; Map[#[[2]] &, Select[Map[{Apply[Plus, #], #} &, Map[t # &, Map[Prepend[#, 1] &, Tuples[{-1, 1}, Length[t] - 1]]]], #[[1]] == s &]]  (* the 5 solutions of using n=10 primes; Peter J. C. Moses, Oct 01 2013 *)

Formula

a(n) = [x^3] Product_{k=4..n+2} (x^prime(k) + 1/x^prime(k)). - Ilya Gutkovskiy, Jan 28 2024

Extensions

Corrected and extended by Clark Kimberling, Oct 01 2013

a(23)-a(49) from Alois P. Heinz, Aug 06 2015