A329443 a(n) is the GCD of the binary representation of n interpreted in any numeric base.

0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 2

Offset

0,7

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

k divides a(A329000(k)) for any k > 0.

Example

For n = 42:
- the binary representation of 42 is "101010",
- the corresponding interpretations in the first bases b, alongside their GCD, are:
  b   b+b^3+b^5  GCD
  --  ---------  ---
   2         42   42
   3        273   21
   4       1092   21
   5       3255   21
   6       7998    3
- as b + b^3 + b^5 is always divisible by 3, we have a(42) = 3.

Prog

(PARI) a(n) = my (g=n, d=binary(n)); for (b=3, oo, g = gcd(g, fromdigits(d, b)); if (g < b, return (g)))

Crossrefs

Cf. A329000, A329126.

Sequence in context: A238097 A066955 A089048 * A348416 A263025 A184348

Adjacent sequences: A329440 A329441 A329442 * A329444 A329445 A329446

Keyword

nonn,base

Author

Rémy Sigrist, Nov 13 2019

Status

approved