A378080 - OEIS

%I #16 Nov 21 2024 09:05:27

%S 0,1,3,4,5,6,7,8,13,14,16,17,18,20,22,23,24,25,26,27,28,29,30,31,32,

%T 33,34,36,39,40,43,45,46,47,48,51,53,54,55,57,58,59,60,61,62,63,64,65,

%U 66,67,68,69,70,71,72,73,74,76,77,79,80,81,82,83,84,85,86,87

%N Nonnegative integers that are not digitally balanced in any integer base b >= 2.

%C A digitally balanced number in base b contains every digit from 0 to b-1 in equal amount.

%C Since the terms in this sequence are not digitally balanced in any base, we could call them "digitally imbalanced numbers".

%H Paolo Xausa, <a href="/A378080/b378080.txt">Table of n, a(n) for n = 1..10000</a>

%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/balanced_number/">Digitally balanced numbers</a>, Numbers Aplenty, 2013.

%t A378080Q[n_] := Module[{b = 1, len}, While[(len = IntegerLength[n, ++b]) >= b && !(Divisible[len, b] && SameQ @@ DigitCount[n, b])]; len < b];

%t Select[Range[0, 150], A378080Q]

%Y Complement of A378073.

%Y Positions of zeros in A378191.

%Y Cf. A378000, A378104.

%K nonn,base

%O 1,3

%A _Paolo Xausa_, Nov 16 2024