OFFSET
1,2
COMMENTS
All terms belong to A059590.
a(n) = n iff n belongs to A059590.
The sequence is well defined: for any n > 0: according to the pigeonhole principle, among the n+1 first repunits in factorial base (A007489), there must be two distinct terms equal modulo n; their absolute difference is a positive multiple of n, and contains only 0's and 1's in factorial base.
This sequence is to factorial base what A004290 is to decimal base.
LINKS
EXAMPLE
The first terms are:
n a(n) a(n) in factorial base
-- ---- ----------------------
1 1 1
2 2 1,0
3 3 1,1
4 8 1,1,0
5 25 1,0,0,1
6 6 1,0,0
7 7 1,0,1
8 8 1,1,0
9 9 1,1,1
10 30 1,1,0,0
11 33 1,1,1,1
12 24 1,0,0,0
13 26 1,0,1,0
14 126 1,0,1,0,0
15 30 1,1,0,0
16 32 1,1,1,0
17 153 1,1,1,1,1
18 126 1,0,1,0,0
19 152 1,1,1,1,0
20 120 1,0,0,0,0
PROG
(PARI) isA059590(n) = my (r=2); while (n, if (n%r > 1, return (0), n\=r; r++)); return (1)
a(n) = forstep (m=n, oo, n, if (isA059590(m), return (m)))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jun 24 2017
STATUS
approved