A394666 a(n) = n! mod (2*n - 1).

0, 2, 1, 3, 3, 5, 9, 0, 15, 9, 0, 12, 0, 0, 6, 16, 0, 0, 34, 0, 25, 21, 0, 23, 0, 0, 38, 0, 0, 30, 36, 0, 0, 33, 0, 36, 50, 0, 0, 39, 0, 42, 0, 0, 17, 0, 0, 0, 11, 0, 96, 51, 0, 54, 71, 0, 64, 0, 0, 0, 0, 0, 0, 63, 0, 65, 0, 0, 87, 70, 0, 0, 0, 0, 22, 76, 0, 0, 143, 0, 0, 81, 0, 84, 0, 0, 40, 0, 0, 89, 81, 0, 0, 0, 0, 95, 137, 0, 190, 99

Offset

1,2

Comments

Conjecturally, a(n) = 0 iff n > 5 and 2*n - 1 is not a prime.

Links

Table of n, a(n) for n=1..100.

Formula

a(n) = n! mod (2*n - 1).

Example

For n = 1: a(1) = 1! mod (2*1 - 1) = 1 mod 1 = 0.
For n = 2: a(2) = 2! mod (2*2 - 1) = 2 mod 3 = 2.
For n = 3: a(3) = 3! mod (2*3 - 1) = 6 mod 5 = 1.

Maple

seq(n! mod (2*n - 1), n=1..100);

Mathematica

Table[Mod[n!, 2*n - 1], {n, 1, 100}]

Prog

(Python)
from math import factorial
print([factorial(n) % (2*n - 1) for n in range(1, 101)])

Crossrefs

Cf. A000142, A005408.

Fixed points are 2*A066160.

Zero points are A104275 (except 5).

Sequence in context: A340623 A059876 A095354 * A132883 A132888 A213934

Adjacent sequences: A394662 A394663 A394664 * A394667 A394668 A394669

Keyword

nonn,easy

Author

Sabuhi A. Amirov, Apr 29 2026

Extensions

More terms from David A. Corneth, Apr 29 2026

Status

approved