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A056792 (Weight of binary expansion of n) + (length of binary expansion of n) - 1 11
0, 1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Minimal number of steps to get from 0 to n by (a) adding 1 or (b) multiplying by 2.

A stopping problem: begin with n and at each stage if even divide by 2 or if odd subtract 1. That is, iterate A029578 while nonzero.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Hugo Pfoertner, Addition chains

Index to sequences related to the complexity of n

FORMULA

a(0) = 0, a(2n+1) = a(2n) + 1 and a(2n) = a(n) + 1.

n>0 a(n)=n-valuation(A000254(n), 2) - Benoit Cloitre, Mar 09 2004

EXAMPLE

12 = 1100 in binary, so a(12)=2+4-1=5.

MATHEMATICA

f[ n_Integer ] := (c = 0; k = n; While[ k != 0, If[ EvenQ[ k ], k /= 2, k-- ]; c++ ]; c); Table[ f[ n ], {n, 0, 100} ]

f[n_] := Floor@ Log2@ n + DigitCount[n, 2, 1]; Array[f, 100] (* Robert G. Wilson v, Jul 31 2012 *)

PROG

(PARI) a(n)=if(n<1, 0, n-valuation(n!*sum(i=1, n, 1/i), 2))

(PARI) a(n)=if(n<1, 0, 1+a(if(n%2, n-1, n/2)))

(PARI) a(n)=n=binary(n); sum(i=1, #n, n[i])+#n-1 \\ Charles R Greathouse IV, Apr 11 2012

CROSSREFS

Equals A056791 - 1. The least inverse (indices of record values) of A056792 is A052955 prepended with 0. See also A014701, A115954, A056796, A056817.

Sequence in context: A060607 A061339 A073933 * A227861 A130500 A072073

Adjacent sequences:  A056789 A056790 A056791 * A056793 A056794 A056795

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 01 2000

EXTENSIONS

More terms from James A. Sellers, Sep 06 2000 and from David W. Wilson, Sep 07, 2000

STATUS

approved

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Last modified April 20 13:52 EDT 2014. Contains 240806 sequences.