A022899 Number of solutions to c(1)*prime(2) + ... + c(n)*prime(n+1) = 2, where c(i) = +-1 for i > 1, c(1) = 1.

0, 0, 0, 1, 0, 0, 0, 4, 0, 9, 0, 14, 0, 75, 0, 155, 0, 724, 0, 2376, 0, 6900, 0, 26937, 0, 92823, 0, 326942, 0, 1156399, 0, 3960856, 0, 14320442, 0, 53136802, 0, 190397836, 0, 706309816, 0, 2596474887, 0, 9540434672, 0, 35480735090, 0, 132003300757, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			a(8) counts these 4 solutions: {3, -5, -7, 11, -13, 17, 19, -23}, {3, -5, -7, 11, 13, -17, -19,  23}, {3, -5, 7, -11, -13, 17, -19, 23}, {3, 5, -7, -11, -13, -17, 19, 23}.
		

Links

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

Programs

Mathematica

{f, s} = {2, 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}]
(* A022899, a(n) = number of solutions of "sum = s" using Prime(f) to Prime(f+n-1) *)
n = 8; 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 4 solutions of using n=8 primes; Peter J. C. Moses, Oct 01 2013 *)

Formula

a(n) = [x^1] Product_{k=3..n+1} (x^prime(k) + 1/x^prime(k)). - Ilya Gutkovskiy, Jan 26 2024

Extensions

Corrected and extended by Clark Kimberling, Oct 01 2013

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