A332635 a(n) = n!! mod prime(n).

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, 65, 54, 40, 71, 54, 62, 85, 122, 114, 1, 40, 4, 87, 45, 126, 172, 53, 93, 109, 139, 28, 167, 78, 19, 222, 182, 136, 230, 231, 110, 163, 264, 45, 92, 134, 177, 241

Offset: 1

Author

Andrew Nelson, Feb 17 2020

Keywords

• nonn
• easy

Comments

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).

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

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

Examples

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

Links

• Andrew Nelson, Table of n, a(n) for n = 1..5000

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = my(p=prime(n)); lift(prod(i=0, (n-1)\2, Mod(n-2*i, p))); \\ Michel Marcus, Feb 25 2020

Formula

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