A130309 Primes of the form [k!! - (k-1)!! + (k-2)!! -....1!!] + 1.

2, 3, 7, 67, 153979499670311863, 96139392052480758114443739387402080695373863

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, May 21 2007

Keywords

• nonn

Comments

The next term is too large to include.

The corresponding values of k are 1, 2, 3, 4, 7, 31, 63, 263, 311, 371, 383, 10243, ... (1 and 2 give the same prime, 2). All these values except 2 and 4 are odd since for k even above 10 this form is divisible by 7. a(11) ~ 2.060 * 10^18317. - Amiram Eldar, Jul 18 2019

Examples

			2 = 1!! + 1 or 2!! - 1!! + 1.
7 = 4!! - 3!! + 2!! - 1!! +1 = 8 - 3 + 2 - 1 + 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10

Crossrefs

Cf. A071828, A130308.

Programs

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[2, 31], PrimeQ] (* Amiram Eldar, Jul 18 2019 *)