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A113040 Number of solutions to +-p(1)+-p(2)+-...+-p(2n)=1 where p(i) is the i-th prime. 11
1, 1, 3, 6, 16, 45, 138, 439, 1417, 4698, 16021, 55146, 190274, 671224, 2404289, 8535117, 30635869, 110496946, 401422210, 1467402238, 5393176633, 19883249002, 73856531314, 273602448261, 1017563027699, 3803902663467, 14266523388813, 53564969402478 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

+-p(1)+-p(2)+-...+-p(2n+1)=1 has no solutions because the l.h.s. is even.

LINKS

Alois P. Heinz and Ray Chandler, Table of n, a(n) for n = 1..1000 (first 130 terms from Alois P. Heinz)

FORMULA

a(n) = A022895(2n) + A261061(n). - M. F. Hasler, Aug 09 2015

Conjecture: limit_{n->infinity} a(n)^(1/n) = 4. - Vaclav Kotesovec, Jun 05 2019

EXAMPLE

2 + 3 + 5 - 7 + 11 - 13 = - 2 + 3 + 5 - 7 - 11 + 13 = - 2 + 3 - 5 + 7 + 11 - 13 = 1 so a(3) = 3.

MAPLE

A113040:=proc(n) local i, j, p, t; t:= NULL; for j from 2 to 2*n by 2 do p:=1; for i to j do p:=p*(x^(-ithprime(i))+x^(ithprime(i))); od; t:=t, coeff(p, x, 1); od; t; end;

# second Maple program:

sp:= proc(n) sp(n):= `if`(n=0, 0, ithprime(n)+sp(n-1)) end:

b := proc(n, i) option remember; `if`(n>sp(i), 0, `if`(i=0, 1,

        b(n+ithprime(i), i-1)+ b(abs(n-ithprime(i)), i-1)))

     end:

a:= n-> b(1, 2*n):

seq(a(n), n=1..40);  # Alois P. Heinz, Aug 05 2012

MATHEMATICA

sp[n_] := If[n == 0, 0, Prime[n]+sp[n-1]]; b[n_, i_] := b[n, i] =If[n > sp[i], 0, If[i == 0, 1, b[n+Prime[i], i-1] + b[Abs[n-Prime[i]], i-1]]]; a[n_] := b[1, 2*n]; Table[a[n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Nov 11 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A083309, A022894 - A022904, A022920, A261057 - A261063 and A261044 - A261045; A215036.

Bisection (even part) of A306443.

Sequence in context: A107269 A086811 A106361 * A244036 A220184 A007002

Adjacent sequences:  A113037 A113038 A113039 * A113041 A113042 A113043

KEYWORD

nonn

AUTHOR

Floor van Lamoen, Oct 12 2005

STATUS

approved

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Last modified August 25 16:17 EDT 2019. Contains 326324 sequences. (Running on oeis4.)