A327226 For any n >= 0, let u and v be such that 2 <= u < v and the digits of n in bases u and v are the same up to a permutation and v is minimized; a(n) = v.
3, 3, 4, 5, 6, 7, 8, 5, 10, 7, 12, 9, 14, 10, 16, 13, 13, 7, 20, 16, 22, 17, 4, 10, 26, 21, 11, 25, 5, 13, 13, 9, 34, 29, 15, 16, 31, 16, 11, 37, 37, 19, 19, 13, 19, 13, 6, 21, 50, 11, 22, 7, 7, 16, 25, 17, 25, 17, 13, 28, 62, 55, 28, 19, 57, 29, 7, 15, 7, 16
Offset: 0
Examples
For n = 11:
- the representations of 11 in bases b = 2..9 are:
b 11 in base b
- ------------
2 "1011"
3 "102"
4 "23"
5 "21"
6 "15"
7 "14"
8 "13"
9 "12"
- the representation in base 9 is the least that shows the same digits, up to order, to some former base, namely the base 5,
- hence a(11) = 9.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
Crossrefs
See A327225 for the corresponding u's.
Programs
-
PARI
a(n) = { my (s=[]); for (v=2, oo, my (d=vecsort(digits(n,v))); if (setsearch(s,d), return (v), s=setunion(s,[d]))) }
Formula
A327225(n) < a(n) <= 1 + max(2, n+1).