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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.
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%I #11 Aug 31 2019 03:09:48

%S 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,

%T 25,5,13,13,9,34,29,15,16,31,16,11,37,37,19,19,13,19,13,6,21,50,11,22,

%U 7,7,16,25,17,25,17,13,28,62,55,28,19,57,29,7,15,7,16

%N 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.

%H Rémy Sigrist, <a href="/A327226/b327226.txt">Table of n, a(n) for n = 0..10000</a>

%F A327225(n) < a(n) <= 1 + max(2, n+1).

%e For n = 11:

%e - the representations of 11 in bases b = 2..9 are:

%e b 11 in base b

%e - ------------

%e 2 "1011"

%e 3 "102"

%e 4 "23"

%e 5 "21"

%e 6 "15"

%e 7 "14"

%e 8 "13"

%e 9 "12"

%e - the representation in base 9 is the least that shows the same digits, up to order, to some former base, namely the base 5,

%e - hence a(11) = 9.

%o (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]))) }

%Y See A327225 for the corresponding u's.

%K nonn,base

%O 0,1

%A _Rémy Sigrist_, Aug 27 2019