A284750 a(n) = least k > 0 such that k * n in factorial base representation contains only 0's and 1's.

1, 1, 1, 2, 5, 1, 1, 1, 1, 3, 3, 2, 2, 9, 2, 2, 9, 7, 8, 6, 6, 33, 256, 1, 1, 1, 1, 26, 5, 1, 1, 1, 1, 149, 24, 4, 159, 4, 130, 3, 3, 3, 3, 118, 16, 128, 16, 3, 3, 3, 3, 14, 16, 16, 840, 13, 89, 15, 88, 2, 2, 12, 2, 2, 78, 11, 13, 76, 597, 12, 71, 2, 2, 555, 2

Offset

1,4

Comments

a(n) = 1 iff n belongs to A059590.

a(a(n)) <= n for any n > 0.

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

Formula

a(n) = A286820(n) / n.

Example

The first terms, alongside n*a(n) in decimal and factorial base, are:
n     a(n)  n*a(n)  n*a(n) in factorial base
--    ----  ------  ------------------------
1     1     1       1
2     1     2       1,0
3     1     3       1,1
4     2     8       1,1,0
5     5     25      1,0,0,1
6     1     6       1,0,0
7     1     7       1,0,1
8     1     8       1,1,0
9     1     9       1,1,1
10    3     30      1,1,0,0
11    3     33      1,1,1,1
12    2     24      1,0,0,0
13    2     26      1,0,1,0
14    9     126     1,0,1,0,0
15    2     30      1,1,0,0
16    2     32      1,1,1,0
17    9     153     1,1,1,1,1
18    7     126     1,0,1,0,0
19    8     152     1,1,1,1,0
20    6     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) = for (k=1, oo, if (isA059590(k*n), return (k)))

Crossrefs

Cf. A059590, A286820.

Sequence in context: A078506 A323909 A124779 * A092134 A181779 A024548

Adjacent sequences: A284747 A284748 A284749 * A284751 A284752 A284753

Keyword

nonn,base

Author

Rémy Sigrist, Jun 25 2017

Status

approved