A130308 Primes of the form [k!! - (k-1)!! + (k-2)!! - ... 1!!] - 1.
5, 317, 1217216458429656137
Offset: 1
Examples
5 = 4!! - 3!! + 2!! - 1!! -1 = 8 - 3 + 2 - 1 - 1.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..6
Programs
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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);
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Mathematica
f[n_] := Sum[(-1)^(n-k)*k!!, {k, 1, n}] - 1; Select[f/@Range[32], PrimeQ] (* Amiram Eldar, Jul 18 2019 *)
Comments