A341691 a(0) = 0, and for any n > 0, a(n) = n - a(k) where k is the greatest number < n such that n AND a(k) = a(k) (where AND denotes the bitwise AND operator).

0, 1, 2, 1, 4, 1, 2, 5, 8, 1, 2, 9, 4, 9, 10, 5, 16, 1, 2, 17, 4, 17, 18, 5, 8, 17, 18, 9, 20, 9, 10, 21, 32, 1, 2, 33, 4, 33, 34, 5, 8, 33, 34, 9, 36, 9, 10, 37, 16, 33, 34, 17, 36, 17, 18, 37, 40, 17, 18, 41, 20, 41, 42, 21, 64, 1, 2, 65, 4, 65, 66, 5, 8, 65

Offset

0,3

Comments

This sequence is a binary variant of A341679; here we look for a term whose binary 1's match those of n, there we look for a term that divides n.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, C program for A341691

Formula

a(n) = n iff n = 0 or n is a power of 2.

a(2*n) = 2*a(n).

Apparently, a(n) = n - a(n - A006519(n)).

Example

The first terms, alongside the corresponding value of k, are:
  n   a(n)  k
  --  ----  ---
   0     0  N/A
   1     1    0
   2     2    0
   3     1    2
   4     4    0
   5     1    4
   6     2    4
   7     5    6
   8     8    0
   9     1    8

Prog

(C) See Links section.

Crossrefs

Cf. A006519, A295989, A341679.

Sequence in context: A171173 A268671 A163618 * A275392 A360329 A106616

Adjacent sequences: A341688 A341689 A341690 * A341692 A341693 A341694

Keyword

nonn,base

Author

Rémy Sigrist, Feb 17 2021

Status

approved