A385485 a(n) is the least number k such that k*n is not a binary Niven number (A049445).

3, 7, 1, 7, 1, 5, 1, 7, 1, 3, 1, 29, 1, 1, 1, 7, 1, 3, 1, 5, 3, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 7, 1, 3, 1, 13, 1, 1, 1, 5, 1, 5, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 17, 1, 1, 1, 7, 1, 3, 1, 7, 3, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 5, 3, 1, 1, 17, 1

Offset: 1

Author

Amiram Eldar, Jun 30 2025

Keywords

• nonn
• easy
• base

Comments

All the terms are odd numbers because if k is even and k*n is not a binary Niven number then so is k*n/2, since A000120(k*n) = A000120(k*n/2).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A049445, A065878, A144262 (decimal analog), A385482, A385486 (indices of records), A385487 (record values).

Programs

Mathematica

a[n_] := Module[{m = n, k = 1}, While[Divisible[m, DigitSum[m, 2]], m += 2*n; k += 2]; k]; Array[a, 100]

PARI

a(n) = {my(m = n, k = 1); while(!(m % hammingweight(m)), m += 2*n; k += 2); k;}

Python

from itertools import count
def a(n): return next(k for k in count(1) if (m:=k*n)%m.bit_count() != 0)
print([a(n) for n in range(1, 86)]) # Michael S. Branicky, Jun 30 2025

Formula

a(n) = 1 if and only if n is in A065878.