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%I #8 Nov 22 2012 13:12:40
%S 3,5,7,13,113,3851,46093,10321937,185794579,
%T 216862434431944426122117120047,
%U 1874480713189654839282450157086195210900931486780353469173376681742503659434414632312033372643386765197475111737132341321962070865661132800000000000000000173
%N Primes of the form n!! + n + 1.
%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 159
%e For n=2, 2!! + 2 + 1 = 2 + 2 + 1 = 5, which is prime;
%e for n=4, 4!! + 4 + 1 = 4*2 + 4 + 1 = 8 + 4 + 1 = 13, which is prime.
%p SFACT:= proc(n) local i,j,k; for k from 1 by 1 to n do i:=k; j:=k-2; while j >0 do i:=i*j; j:=j-2; od: if isprime(i+k+1) then print(i+k+1); fi; od: end: SFACT(550);
%t Select[Table[n!!+n+1,{n,250}],PrimeQ] (* _Harvey P. Dale_, Nov 22 2012 *)
%K nonn
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 22 2006