login
This site is supported by donations to The OEIS Foundation.
Logo

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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; 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

Hugo Pfoertner, Addition chains

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 (benoit7848c(AT)orange.fr), 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} ]

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)))

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 * A130500 A072073 A061716

Adjacent sequences:  A056789 A056790 A056791 * A056793 A056794 A056795

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Sep 01 2000

EXTENSIONS

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 06 2000 and from David W. Wilson (davidwwilson(AT)comcast.net), Sep 07, 2000

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified February 16 19:20 EST 2012. Contains 205945 sequences.