OFFSET
1,5
COMMENTS
There cannot be a solution for an even number of terms on the l.h.s. because all terms are odd but the r.h.s. is odd, too.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..300
FORMULA
a(n) = [x^4] Product_{k=3..2*n} (x^prime(k) + 1/x^prime(k)). - Ilya Gutkovskiy, Jan 31 2024
EXAMPLE
a(1) = a(2) = 0 because prime(2) and prime(2) +- prime(3) +- prime(4) are always different from -1.
a(3) = 1 because the solution prime(2) + prime(3) - prime(4) + prime(5) - prime(6) = -1 is the only one involving prime(2) through prime(6).
MAPLE
s:= proc(n) option remember;
`if`(n<3, 0, ithprime(n)+s(n-1))
end:
b:= proc(n, i) option remember; `if`(n>s(i), 0, `if`(i=2, 1,
b(abs(n-ithprime(i)), i-1)+b(n+ithprime(i), i-1)))
end:
a:= n-> b(4, 2*n):
seq(a(n), n=1..30); # Alois P. Heinz, Aug 08 2015
MATHEMATICA
s[n_] := s[n] = If[n < 3, 0, Prime[n] + s[n-1]];
b[n_, i_] := b[n, i] = If[n > s[i], 0, If[i == 2, 1, b[Abs[n-Prime[i]], i-1] + b[n+Prime[i], i-1]]];
a[n_] := b[4, 2n];
Array[a, 30] (* Jean-François Alcover, Nov 07 2020, after Alois P. Heinz *)
PROG
(PARI) A261062(n, rhs=-1, firstprime=2)={rhs-=prime(firstprime); my(p=vector(2*n-2+bittest(rhs, 0), i, prime(i+firstprime))); sum(i=1, 2^#p-1, sum(j=1, #p, (-1)^bittest(i, j-1)*p[j])==rhs)} \\ For illustrative purpose; too slow for n >> 10.
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Aug 08 2015
EXTENSIONS
a(14)-a(29) from Alois P. Heinz, Aug 08 2015
STATUS
approved