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

1,2

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, ... .

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A057597 A226392 A121340 * A358664 A231206 A165241

Adjacent sequences: A332632 A332633 A332634 * A332636 A332637 A332638

Keyword

nonn,easy

Author

Andrew Nelson, Feb 17 2020

Status

approved