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.
%I A130308 #9 Jul 18 2019 14:29:05
%S A130308 5,317,1217216458429656137
%N A130308 Primes of the form [k!! - (k-1)!! + (k-2)!! - ... 1!!] - 1.
%C A130308 The next term is too large to include.
%C A130308 The corresponding values of k are 4, 8, 32, 180, 264, 328, 1788, 2308, 5152, 7572, 13496, ... ; all these values are even since for k odd above 11 this form is divisible by 7. - _Amiram Eldar_, Jul 18 2019
%H A130308 Amiram Eldar, <a href="/A130308/b130308.txt">Table of n, a(n) for n = 1..6</a>
%e A130308 5 = 4!! - 3!! + 2!! - 1!! -1 = 8 - 3 + 2 - 1 - 1.
%p A130308 P:=proc(n) local a,i,j,k,w; for i from 1 by 1 to n do a:=0; for j from i by -1 to 0 do k:=j; w:=j-2; while w>0 do k:=k*w; w:=w-2; od; a:=a+k*(-1)^j od; if isprime(abs(a)-1) then print(abs(a)-1); fi; od; end: P(1000);
%t A130308 f[n_] := Sum[(-1)^(n-k)*k!!, {k, 1, n}] - 1; Select[f/@Range[32], PrimeQ] (* _Amiram Eldar_, Jul 18 2019 *)
%Y A130308 Cf. A071828, A130309.
%K A130308 nonn,bref
%O A130308 1,1
%A A130308 _Paolo P. Lava_ and _Giorgio Balzarotti_, May 21 2007