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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).
10
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
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. 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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 14 2015
STATUS
approved