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A086330
a(n) = Sum_{m >= 2} m! mod n.
3
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.
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
KEYWORD
easy,nonn
AUTHOR
Walter Carlini, Aug 31 2003
EXTENSIONS
Corrected and extended by Vladeta Jovovic, Sep 06 2003
STATUS
approved