A022901 Number of solutions to c(1)*prime(3)+...+c(n)*prime(n+2) = 1, where c(i) = +-1 for i>1, c(1) = 1.

0, 0, 1, 0, 0, 0, 3, 0, 3, 0, 6, 0, 35, 0, 88, 0, 351, 0, 1144, 0, 3570, 0, 13281, 0, 45712, 0, 161985, 0, 574357, 0, 1993704, 0, 7191396, 0, 26481567, 0, 95441234, 0, 352520549, 0, 1296413520, 0, 4775354550, 0, 17754091585, 0, 65964401274, 0, 245645895029, 0

Offset

1,7

Links

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

Formula

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

Example

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

Mathematica

{f, s} = {3, 1}; 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}]
(* A022901, a(n) = number of solutions of "sum = s" using Prime(f) to Prime(f+n-1) *)
n = 7; 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 3 solutions of using n=7 primes; Peter J. C. Moses, Oct 01 2013 *)

Crossrefs

Sequence in context: A100258 A045763 A132748 * A348215 A331739 A356169

Adjacent sequences: A022898 A022899 A022900 * A022902 A022903 A022904

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected and extended by Clark Kimberling, Oct 01 2013

a(23)-a(50) from Alois P. Heinz, Aug 06 2015

Status

approved