A378191 a(n) is the number of integer bases >= 2 in which n is digitally balanced.

0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Giovanni Resta, Digitally balanced numbers, Numbers Aplenty, 2013.

Formula

a(A378080(n+1)) = 0.

a(A378073(n)) >= 1 for n >= 1.

a(A065963(n)) = n for n >= 1.

Example

a(n) = 1 for the first time at n = A065963(1) = 2 = 10_2.
a(n) = 2 for the first time at n = A065963(2) = 135 = 10000111_2 = 2013_4.
a(n) = 3 for the first time at n = A065963(3) = 13575 = 11010100000111_2 = 200121210_3 = 142503_6.

Mathematica

A378191[n_] := Module[{b = 1, c = 0, len}, While[(len = IntegerLength[n, ++b]) >= b, If[Divisible[len, b] && SameQ@@DigitCount[n, b], c++]]; c];
Array[A378191, 100, 0]

Crossrefs

Cf. A049364, A065963, A378000, A378073, A378080, A378104.

Sequence in context: A289104 A289235 A188371 * A353489 A288106 A286939

Adjacent sequences: A378188 A378189 A378190 * A378192 A378193 A378194

Keyword

nonn,base

Author

Paolo Xausa, Nov 19 2024

Status

approved