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

1,2

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

Rémy Sigrist, Table of n, a(n) for n = 1..2000

Wikipedia, Factorial number system

Index entries for sequences related to factorial base representation

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

Cf. A004290, A007489, A059590, A284750.

Sequence in context: A120260 A202592 A002619 * A129202 A127905 A277040

Adjacent sequences: A286817 A286818 A286819 * A286821 A286822 A286823

Keyword

nonn,base

Author

Rémy Sigrist, Jun 24 2017

Status

approved