A091858 -id:A091858 - cp's OEIS frontend

A067999 Numbers k such that (k! - 1) == 0 (mod prime(k)).

1, 3, 10, 149, 437

Offset: 1

Robert G. Wilson v, Feb 08 2002

There are no more terms through 5000000. - Ryan Propper, Dec 30 2007

Numbers k such that A091858(k) = 1. - Zak Seidov, Oct 05 2012

f[n_] := Block[{k = p = 1, m = Prime[n]}, While[p = Mod[p k, m]; k < n, k++ ]; p]; Do[ If[ f[n] == 1, Print[n]], {n, 100000}] (* Robert G. Wilson v, Mar 16 2004 *)

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

Original entry on oeis.org

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

Andrew Nelson, Feb 17 2020

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, ... .

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

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

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

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

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

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

cp's OEIS Frontend

A067999 Numbers k such that (k! - 1) == 0 (mod prime(k)).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula