A255072 Number of steps to reach 0 starting with n and using the iterated process: x -> x - (number of runs in binary representation of x).

0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 25

Offset: 0

Author

Antti Karttunen, Feb 14 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A255053 (least inverse), A255055 (greatest inverse), A255054 (run lengths).

Cf. A005811, A236840, A255071, A255056.

Cf. A255061 & A255062 (values at points (2^n)-2 and (2^n)-1).

Analogous sequences: A071542, A219642, A219652

Formula

a(0) = 0; for n >= 1, a(n) = 1 + a(A236840(n)) = 1 + a(n - A005811(n)).

Other identities. For all n >= 0:

a(A255053(n)) = a(A255055(n)) = n.

a(A255056(n)) = n. [This sequence works also as an inverse function for number-of-runs beanstalk A255056.]