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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).
1
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
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 17 2021
STATUS
approved