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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A292699 Number of solutions to 5 +- 11 +- 17 +- 23 +- ... +- prime(4*n+1) = 0.

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%I A292699 #24 Apr 30 2022 07:57:59
%S A292699 0,1,1,2,2,5,28,102,242,835,3381,10115,39415,138555,465778,1741167,
%T A292699 6081563,22156403,81090107,301185788,1098440558,4071519963,
%U A292699 15235221189,56764430821,211797564907,790029575790,2962705350767,11154931819979,42097079364709
%N A292699 Number of solutions to 5 +- 11 +- 17 +- 23 +- ... +- prime(4*n+1) = 0.
%H A292699 Seiichi Manyama, <a href="/A292699/b292699.txt">Table of n, a(n) for n = 1..200</a>
%F A292699 Constant term in the expansion of 1/2 * Product_{k=1..2*n} (x^prime(2*k+1) + 1/x^prime(2*k+1)).
%e A292699 For n=2 the solution is 5-11-17+23 = 0.
%e A292699 For n=3 the solution is 5+11+17-23+31-41 = 0.
%e A292699 For n=4 the 2 solutions are 5-11+17+23+31+41-47-59 = 0 and 5+11-17+23+31-41+47-59 = 0.
%p A292699 s:= proc(n) s(n):= `if`(n=0, 0, ithprime(2*n+1)+s(n-1)) end:
%p A292699 b:= proc(n, i) option remember; `if`(n>s(i), 0, `if`(i=0, 1,
%p A292699       (p-> b(n+p, i-1)+b(abs(n-p), i-1))(ithprime(2*i+1))))
%p A292699     end:
%p A292699 a:= n-> b(0, 2*n)/2:
%p A292699 seq(a(n), n=1..30);  # _Alois P. Heinz_, Sep 21 2017
%t A292699 s[n_] := s[n] = If[n == 0, 0, Prime[2n+1] + s[n-1]];
%t A292699 b[n_, i_] := b[n, i] = If[n > s[i], 0, If[i == 0, 1,
%t A292699      With[{p = Prime[2i+1]}, b[n+p, i-1] + b[Abs[n-p], i-1]]]];
%t A292699 a[n_] := b[0, 2n]/2;
%t A292699 Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Apr 30 2022, after _Alois P. Heinz_ *)
%o A292699 (PARI) {a(n) = 1/2*polcoeff(prod(k=1, 2*n, x^prime(2*k+1)+1/x^prime(2*k+1)), 0)}
%Y A292699 Cf. A000040, A022894, A083309, A292698, A292700.
%K A292699 nonn
%O A292699 1,4
%A A292699 _Seiichi Manyama_, Sep 21 2017