

A327225


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) = u.


2



2, 2, 3, 4, 5, 6, 7, 3, 9, 4, 11, 5, 13, 4, 15, 7, 5, 5, 19, 6, 21, 5, 3, 7, 25, 6, 6, 13, 4, 9, 7, 7, 33, 8, 8, 11, 7, 7, 7, 19, 13, 13, 10, 10, 7, 7, 5, 9, 49, 9, 8, 5, 4, 10, 13, 13, 9, 9, 9, 19, 61, 10, 10, 10, 9, 9, 5, 9, 6, 13, 11, 11, 73, 10, 9, 12, 9
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

For any n >= 0, the sequence is well defined as the representation of n in any base b >= max(2, n+1) corresponds to a single digit n.
(n, u = A327225(n), v = A327226(n)) = (n, n+1, n+2) iff n = 1 or n is in A059809.  Bernard Schott, Aug 31 2019


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10000


FORMULA

a(n) <= max(2, n+1).


EXAMPLE

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) = 5.


PROG

(PARI) a(n) = { my (s=[]); for (v=2, oo, my (d=vecsort(digits(n, v))); if (setsearch(s, d), forstep (u=v1, 2, 1, if (vecsort(digits(n, u))==d, return (u))), s=setunion(s, [d]))) }


CROSSREFS

See A327226 for the corresponding v's.
Cf. A004053, A059809.
Sequence in context: A251629 A279033 A304744 * A071754 A266113 A078171
Adjacent sequences: A327222 A327223 A327224 * A327226 A327227 A327228


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Aug 27 2019


STATUS

approved



