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A286820
a(n) = smallest positive multiple of n whose factorial base representation contains only 0's and 1's.
2
1, 2, 3, 8, 25, 6, 7, 8, 9, 30, 33, 24, 26, 126, 30, 32, 153, 126, 152, 120, 126, 726, 5888, 24, 25, 26, 27, 728, 145, 30, 31, 32, 33, 5066, 840, 144, 5883, 152, 5070, 120, 123, 126, 129, 5192, 720, 5888, 752, 144, 147, 150, 153, 728, 848, 864, 46200, 728
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.
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