A378080 Nonnegative integers that are not digitally balanced in any integer base b >= 2.

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, 33, 34, 36, 39, 40, 43, 45, 46, 47, 48, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87

Offset: 1

Author

Paolo Xausa, Nov 16 2024

Keywords

• nonn
• base

Comments

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

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

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Giovanni Resta, Digitally balanced numbers, Numbers Aplenty, 2013.

Crossrefs

Complement of A378073.

Positions of zeros in A378191.

Cf. A378000, A378104.

Programs

Mathematica

A378080Q[n_] := Module[{b = 1, len}, While[(len = IntegerLength[n, ++b]) >= b && !(Divisible[len, b] && SameQ @@ DigitCount[n, b])]; len < b];
Select[Range[0, 150], A378080Q]