A086330 a(n) = Sum_{m >= 2} m! mod n.

0, 2, 4, 7, 2, 18, 8, 17, 12, 43, 8, 73, 32, 17, 24, 113, 26, 159, 12, 32, 76, 203, 8, 112, 164, 89, 60, 334, 32, 496, 88, 164, 232, 67, 44, 706, 292, 164, 32, 863, 74, 874, 164, 62, 456, 1097, 56, 291, 162, 317, 268, 1124, 116, 142, 88, 425, 566, 1560, 32, 2033, 930

Offset

2,2

Comments

A discrete infinite sum that has some rough analogies to the infinite series for exponentials.

Links

Table of n, a(n) for n=2..62.

Formula

a(n) = -1 + Sum_{k=1..n} A062169(n, k). - Vladeta Jovovic, Sep 06 2003

Example

a(7) = 2! mod 7 + 3! mod 7 + 4! mod 7 + 5! mod 7 + 6! mod 7 + 7! mod 7 + 8! mod 7 + . . . = 2 mod 7 + 6 mod 7 + 24 mod 7 + 120 mod 7 + 720 mod 7 + 5040 mod 7 + 40320 mod 7 + ... = 2 + 6 + 3 + 1 + 6 + (all further values are zero) = 18.

Prog

(PARI) a(n) = sum(m=2, n, m! % n) \\ Michel Marcus, Jul 23 2013
(Python)
def A086330(n):
    a, c = 0, 1
    for m in range(2, n):
        c = c*m%n
        if c==0:
            break
        a += c
    return a # Chai Wah Wu, Apr 16 2024

Crossrefs

Cf. A062169.

Sequence in context: A166531 A133292 A126218 * A098283 A373786 A359005

Adjacent sequences: A086327 A086328 A086329 * A086331 A086332 A086333

Keyword

easy,nonn

Author

Walter Carlini, Aug 31 2003

Extensions

Corrected and extended by Vladeta Jovovic, Sep 06 2003

Status

approved