A332635 - OEIS

%I #31 Apr 23 2020 22:39:49

%S 1,2,3,1,4,9,3,4,2,12,10,15,40,34,9,11,3,28,50,55,15,24,31,80,8,16,86,

%T 65,54,40,71,54,62,85,122,114,1,40,4,87,45,126,172,53,93,109,139,28,

%U 167,78,19,222,182,136,230,231,110,163,264,45,92,134,177,241

%N a(n) = n!! mod prime(n).

%C a(n) > 0, as n!! cannot be divisible by prime(n): n < prime(n) for all n, so the prime factorization of n!! never includes prime(n).

%C a(n) = 1 for n = 1, 4, 37, 2721, ... .

%C a(n) = n for n = 1, 2, 3, 86, 122, ... .

%H Andrew Nelson, <a href="/A332635/b332635.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = n!! mod prime(n), where n!! denotes the double factorial of n.

%e For n = 4, a(4) = 4!! mod prime(4) = 8 mod 7 = 1.

%t Table[Mod[n!!, Prime[n]], {n, 100}]

%o (PARI) a(n) = my(p=prime(n)); lift(prod(i=0, (n-1)\2, Mod(n-2*i, p))); \\ _Michel Marcus_, Feb 25 2020

%Y Cf. A000040 (primes), A006882 (double factorials), A091858 (n! mod prime(n)).

%K nonn,easy

%O 1,2

%A _Andrew Nelson_, Feb 17 2020