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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. 1

%I

%S 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,

%T 0,161985,0,574357,0,1993704,0,7191396,0,26481567,0,95441234,0,

%U 352520549,0,1296413520,0,4775354550,0,17754091585,0,65964401274,0,245645895029,0

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

%H Alois P. Heinz, <a href="/A022901/b022901.txt">Table of n, a(n) for n = 1..500</a>

%e 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}.

%t {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}]

%t (* A022901, a(n) = number of solutions of "sum = s" using Prime(f) to Prime(f+n-1) *)

%t 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 *)

%K nonn

%O 1,7

%A _Clark Kimberling_

%E Corrected and extended by _Clark Kimberling_, Oct 01 2013

%E a(23)-a(50) from _Alois P. Heinz_, Aug 06 2015

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Last modified February 25 21:00 EST 2020. Contains 332258 sequences. (Running on oeis4.)