A284750 -id:A284750 - cp's OEIS frontend

A286820 a(n) = smallest positive multiple of n whose factorial base representation contains only 0's and 1's.

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

Rémy Sigrist, Jun 24 2017

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.

			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

Rémy Sigrist, Table of n, a(n) for n = 1..2000
Wikipedia, Factorial number system
Index entries for sequences related to factorial base representation

Cf. A004290, A007489, A059590, A284750.

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)))

cp's OEIS Frontend

A286820 a(n) = smallest positive multiple of n whose factorial base representation contains only 0's and 1's.

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