A111412 a(n) = f(f(n+1))-f(f(n)), where f(m) = wt(m) = A000120(m).

1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 0, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, -1, 1, -1

Offset

0,128

Links

Zhuorui He, Table of n, a(n) for n = 0..10000

Mathematica

f[n_] := DigitCount[n, 2, 1]; a[n_] := f[f[n+1]] - f[f[n]]; Array[a, 100, 0] (* Amiram Eldar, Jul 23 2023 *)

Prog

(PARI) A111412(n) = hammingweight(hammingweight(n+1)) - hammingweight(hammingweight(n)) \\ Zhuorui He, Dec 05 2025

Crossrefs

Cf. A000120.

First differences of A054868.

Sequence in context: A266243 A266608 A333818 * A080111 A204545 A185116

Adjacent sequences: A111409 A111410 A111411 * A111413 A111414 A111415

Keyword

sign,base

Author

N. J. A. Sloane, Nov 12 2005

Extensions

Definition corrected by N. J. A. Sloane, Feb 14 2018

Status

approved