A266161 Hamming weights of A266089.

0, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 3, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 4, 5, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 3, 2, 3, 4, 3

Offset: 0

Author

Reinhard Zumkeller, Dec 22 2015

Keywords

• nonn
• base

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000120, A140253, A266089.

Programs

Haskell

a266161 = a000120 . a266089

Mathematica

s[0] = 0; s[n_] := s[n] = Module[{bw = DigitCount[s[n - 1], 2, 1], k = 1}, While[!FreeQ[Array[s, n - 1], k] || Abs[DigitCount[k, 2, 1] - bw] != 1, k++]; k]; DigitCount[Array[s, 100, 0], 2, 1] (* Amiram Eldar, Jul 18 2023 *)

Formula

a(n) = A000120(A266089(n)).

abs(a(n+1) - a(n)) = 1 by definition of A266089.

For n > 0: a(A140253(n)) = n and a(m) < n for m < A140253(n).