|
|
A130308
|
|
Primes of the form [k!! - (k-1)!! + (k-2)!! - ... 1!!] - 1.
|
|
2
|
|
|
|
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
|
|
|
KEYWORD
|
nonn,bref
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|