cp's OEIS Frontend

A378073 Positive integers that are digitally balanced in some integer base b >= 2.

%I A378073 #16 Nov 21 2024 09:05:22
%S A378073 2,9,10,11,12,15,19,21,35,37,38,41,42,44,49,50,52,56,75,78,99,108,114,
%T A378073 120,135,139,141,142,147,149,150,153,154,156,163,165,166,169,170,172,
%U A378073 177,178,180,184,195,197,198,201,202,204,209,210,212,216,225,226,228
%N A378073 Positive integers that are digitally balanced in some integer base b >= 2.
%C A378073 A digitally balanced number in base b contains every digit from 0 to b-1 in equal amount.
%C A378073 This is the set of all of the distinct terms in A378000.
%H A378073 Paolo Xausa, <a href="/A378073/b378073.txt">Table of n, a(n) for n = 1..10000</a>
%H A378073 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/balanced_number/">Digitally balanced numbers</a>, Numbers Aplenty, 2013.
%e A378073 99 is a term because it's a digitally balanced number in base 5 (99 = 12034_5).
%e A378073 135 is a term because it's a digitally balanced number in two bases (135 = 10000111_2 = 2013_4).
%t A378073 A378073Q[n_] := Module[{b = 1, len}, While[(len = IntegerLength[n, ++b]) >= b && !(Divisible[len, b] && SameQ @@ DigitCount[n, b])]; len >= b];
%t A378073 Select[Range[500], A378073Q]
%Y A378073 Cf. A049364, A061845, A065963, A378000, A378080 (complement).
%Y A378073 Supersequence of A378104.
%Y A378073 Positions of positive terms in A378191.
%K A378073 nonn,base
%O A378073 1,1
%A A378073 _Paolo Xausa_, Nov 16 2024