A378104 Positive integers that are digitally balanced in more than one integer base b >= 2.

135, 141, 147, 156, 177, 180, 198, 201, 210, 216, 225, 228, 572, 678, 684, 714, 722, 738, 2110, 2170, 2230, 2382, 2410, 2638, 2702, 2710, 2758, 2830, 2886, 8287, 8351, 8367, 8375, 8399, 8415, 8429, 8435, 8479, 8527, 8539, 8551, 8563, 8569, 8591, 8605, 8615, 8619, 8630

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.

Examples

			135 is a term because it's a digitally balanced number in two bases (135 = 10000111_2 = 2013_4).
The first term that is digitally balanced in three bases is 13575 = 11010100000111_2 = 200121210_3 = 142503_6.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000
• Giovanni Resta, Digitally balanced numbers, Numbers Aplenty, 2013.

Crossrefs

Subsequence of A378073.

Cf. A049364, A065963, A378000, A378104.

Programs

Mathematica

A378104Q[n_] := Module[{b = 1, c = 0, len}, While[(len = IntegerLength[n, ++b]) >= b, If[Divisible[len, b] && SameQ @@ DigitCount[n, b], c++]]; c > 1];
Select[Range[10000], A378104Q]