A255061 Number of steps to reach 0 when starting from (2^n)-2 and iterating the map x -> x - (number of runs in binary representation of x): a(n) = A255072(A000918(n)).

0, 1, 3, 6, 11, 20, 36, 65, 118, 215, 393, 721, 1329, 2463, 4589, 8590, 16142, 30434, 57549, 109114, 207388, 395045, 754027, 1441971, 2762764, 5303466, 10200385, 19656528, 37948281, 73384080, 142115376, 275551755, 534790472, 1038702980, 2018626772, 3924923937, 7634733312

Offset: 1

Author

Antti Karttunen, Feb 14 2015

Keywords

• nonn

Comments

Apart from a(1)=1, also gives the positions of ones in A255054.

Crossrefs

One less than A255062.

First differences: A255071.

Apart from a(1)=1, a subsequence of A255059.

Cf. A000918, A255072, A255054.

Analogous sequences: A218600, A226061.

Programs

Scheme

(define (A255061 n) (A255072 (A000918 n)))
(define (A255061 n) (if (= 1 n) 0 (+ (A255061 (- n 1)) (A255071 (- n 1))))) ;; Assuming that A255071 has been already computed, with e.g. the PARI-program given in that entry.

Formula

a(n) = A255072(A000918(n)).

a(1) = 0; for n > 1, a(n) = a(n-1) + A255071(n-1).

Other identities. For all n >= 1:

a(n) = A255062(n) - 1.