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

2, 9, 10, 11, 12, 15, 19, 21, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 75, 78, 99, 108, 114, 120, 135, 139, 141, 142, 147, 149, 150, 153, 154, 156, 163, 165, 166, 169, 170, 172, 177, 178, 180, 184, 195, 197, 198, 201, 202, 204, 209, 210, 212, 216, 225, 226, 228

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.

This is the set of all of the distinct terms in A378000.

Examples

			99 is a term because it's a digitally balanced number in base 5 (99 = 12034_5).
135 is a term because it's a digitally balanced number in two bases (135 = 10000111_2 = 2013_4).
		

Links

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

Crossrefs

Cf. A049364, A061845, A065963, A378000, A378080 (complement).

Supersequence of A378104.

Positions of positive terms in A378191.

Programs

Mathematica

A378073Q[n_] := Module[{b = 1, len}, While[(len = IntegerLength[n, ++b]) >= b && !(Divisible[len, b] && SameQ @@ DigitCount[n, b])]; len >= b];
Select[Range[500], A378073Q]