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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

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

EXAMPLE

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}.

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 *)

CROSSREFS

Sequence in context: A187172 A241667 A259258 * A081148 A187606 A138478

Adjacent sequences:  A022896 A022897 A022898 * A022900 A022901 A022902

KEYWORD

nonn,changed

AUTHOR

Clark Kimberling

EXTENSIONS

Corrected and extended by Clark Kimberling, Oct 01 2013

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

STATUS

approved

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Last modified December 5 21:40 EST 2016. Contains 278771 sequences.