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%I #7 Apr 15 2018 07:53:59
%S 3,17,29,281,254993,690953,607435538171963,
%T 192133794380608031505991200873083839505054136751452696277424837839455632569607117048950195313
%N Primes of the form [n! mod (n!!+1)]/2, with n>=1.
%C The next term has 611 digits. - _Harvey P. Dale_, Apr 15 2018
%e n=6 n!=720 n!!=48 [n! mod (n!!+1)]/2 = (720 mod 49)/2 = 34/2 = 17
%e n=7 n!=5040 n!!=105 [n! mod (n!!+1)]/2 = (5040 mod 106)/2 = 58/2 = 29
%p P:=proc(n) local i,j,k,w; for i from 2 by 1 to n do k:=i; w:=i-2; while w>0 do k:=k*w; w:=w-2; od; j:=(i! mod (k+1))/2; if isprime(j) then print(j); fi; od; end: P(1000);
%t Select[Table[Mod[n!,n!!+1]/2,{n,200}],PrimeQ] (* _Harvey P. Dale_, Apr 15 2018 *)
%Y Cf. A055490.
%K hard,nonn
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Mar 14 2007
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