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

1,1

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A383432 A354977 A080172 * A133065 A335815 A021733

Adjacent sequences: A385482 A385483 A385484 * A385486 A385487 A385488

Keyword

nonn,easy,base

Author

Amiram Eldar, Jun 30 2025

Status

approved