A130308 Primes of the form [k!! - (k-1)!! + (k-2)!! - ... 1!!] - 1.

5, 317, 1217216458429656137

Offset

1,1

Comments

The next term is too large to include.

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..6

Example

5 = 4!! - 3!! + 2!! - 1!! -1 = 8 - 3 + 2 - 1 - 1.

Maple

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);

Mathematica

f[n_] := Sum[(-1)^(n-k)*k!!, {k, 1, n}] - 1; Select[f/@Range[32], PrimeQ] (* Amiram Eldar, Jul 18 2019 *)

Crossrefs

Cf. A071828, A130309.

Sequence in context: A160071 A094161 A366305 * A304212 A212041 A251696

Adjacent sequences: A130305 A130306 A130307 * A130309 A130310 A130311

Keyword

nonn,bref

Author

Paolo P. Lava and Giorgio Balzarotti, May 21 2007

Status

approved