OFFSET
1,5
COMMENTS
The first occurrences for 0..10 are 1, 2, 5, 29, 17, 23, 199, 619, 3313, 4093, 3011, ... (see A049050). - Antti Karttunen, Oct 01 2018
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..12021
EXAMPLE
From Antti Karttunen, Oct 01 2018: (Start)
a(1) = 0 because 1 divides all factorial numbers (A000142): 1, 2, 6, 24, ... and thus there are no cases where the remainder would be 1.
a(3) = 1 as (1! mod 3) = 1, (2! mod 3) = 2 and for 3! and larger factorials the remainder is always 0. Thus there is exactly one case where the remainder is one.
a(5) = 2 as (1! mod 5) = 1, (2! mod 5) = 2, (3! mod 5) = 1, (4! mod 5) = 5, (5! mod 5) = 0, and so on ever after for larger factorials.
(End)
MATHEMATICA
Table[Length[Select[Range[100], Mod[#!, n] == 1 &]], {n, 1, 100}] (* G. C. Greubel, Oct 08 2018 *)
PROG
(PARI) A049046(n) = { my(s=0, r, k=1); while((r=(k! % n))>0, s += (1==r); k++); (s); }; \\ Antti Karttunen, Oct 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Term a(1) corrected and the definition clarified by Antti Karttunen, Oct 01 2018
Definition further edited by Antti Karttunen, Oct 06 2018, based on feedback from David W. Wilson
STATUS
approved