A351599 a(n) is the smallest integer m > 0 such that m*n is a digitally balanced number (A031443).

2, 1, 3, 3, 2, 2, 5, 7, 1, 1, 4, 1, 4, 3, 9, 15, 9, 10, 2, 9, 2, 2, 8, 9, 2, 2, 5, 2, 8, 5, 17, 31, 5, 5, 1, 5, 1, 1, 4, 6, 1, 1, 4, 1, 3, 4, 3, 5, 1, 1, 3, 1, 4, 4, 3, 1, 4, 4, 3, 3, 13, 9, 33, 63, 3, 3, 3, 3, 10, 3, 2, 3, 11, 9, 2, 3, 2, 2, 8, 3, 10, 9, 2

Offset: 1

Author

Alex Ratushnyak, May 02 2022

Keywords

• nonn
• base

Crossrefs

Cf. A031443, A143146.

Programs

Mathematica

balQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ@(m = Length@d) && Count[d, 1] == m/2]; a[n_] := Module[{k = 1}, While[!balQ[k*n], k++]; k]; Array[a, 100] (* Amiram Eldar, May 02 2022 *)

PARI

is(n) = hammingweight(n)==hammingweight(bitneg(n, #binary(n))); \\ A031443
a(n) = my(m=1); while (!is(m*n), m++); m; \\ Michel Marcus, May 02 2022

Formula

a(n) = A143146(n) / n. - Rémy Sigrist, Jul 11 2022