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A130308 Primes of the form [k!! - (k-1)!! + (k-2)!! - ... 1!!] - 1. 2
5, 317, 1217216458429656137 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A160071 A094161 A366305 * A304212 A212041 A251696
KEYWORD
nonn,bref
AUTHOR
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)