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

0,4

Links

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

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.]

Prog

(Scheme, with memoization-macro definec)
(definec (A255072 n) (if (zero? n) 0 (+ 1 (A255072 (A236840 n)))))

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

Sequence in context: A060973 A352228 A097915 * A029131 A162351 A087816

Adjacent sequences: A255069 A255070 A255071 * A255073 A255074 A255075

Keyword

nonn

Author

Antti Karttunen, Feb 14 2015

Status

approved