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A101279 a(1) = 1; a(2k) = a(k), a(2k+1) = k. 5
1, 1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 6, 3, 7, 1, 8, 4, 9, 2, 10, 5, 11, 1, 12, 6, 13, 3, 14, 7, 15, 1, 16, 8, 17, 4, 18, 9, 19, 2, 20, 10, 21, 5, 22, 11, 23, 1, 24, 12, 25, 6, 26, 13, 27, 3, 28, 14, 29, 7, 30, 15, 31, 1, 32, 16, 33, 8, 34, 17, 35, 4, 36, 18, 37, 9, 38, 19, 39, 2, 40, 20, 41, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

From Jeremy Gardiner, Mar 22 2015: (Start)

For n>2 write n, n-1 in binary then align bits from the left and take contiguous matching bits as a binary number.

For example:

n    = 19 10011

n-1  = 18 10010

a(n) =  9 1001

Also arrange the positive integers as a binary tree rooted at 1 as shown:

                                     1

                                     |

                 2................../ \..................3

                 |                                       |

       4......../ \........5                   6......../ \........7

      / \                 / \                 / \                 / \

     /   \               /   \               /   \               /   \

    /     \             /     \             /     \             /     \

   8       9          10      11          12       13         14       15

16 17   18 19      20  21  22  23      24  25   26  27     28  29   30  31

Each branch doubles the number above at the left fork or doubles and adds 1 at the right fork. Then for n>2, a(n) is the greatest common ancestor of n and n-1, a(n) = gca(n,n-1).

(End)

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a((n+1)/2) = A028310(n) if n is odd and a(n/2)=a(n) if n is even; thus this is a fractal sequence. - Robert G. Wilson v, May 23 2006; corrected by Clark Kimberling, Jul 07 2007

a(n) = A025480(n) + A036987(n) = (n/2^A007814(n)-1)/2 + (n == 2^A007814(n)). - Ralf Stephan, Aug 21 2013

EXAMPLE

If n is a power of 2 then k=1.

MAPLE

a:=array(0..200); a[1]:=1; M:=200; for n from 2 to M do if n mod 2 = 1 then a[n]:=(n-1)/2; else a[n]:=a[n/2]; fi; od: [seq(a[n], n=1..M)];

MATHEMATICA

a[1] = 1; a[n_] := a[n] = If[OddQ@n, (n - 1)/2, a[n/2]]; Array[a, 84] (* Robert G. Wilson v, May 23 2006 *)

PROG

(PARI) a(n)=(n/2^valuation(n, 2)-1)/2+if(n==2^valuation(n, 2), 1, 0) /* Ralf Stephan, Aug 21 2013 */

CROSSREFS

Cf. A003602, A025480.

Sequence in context: A130747 A055440 A250028 * A064576 A322390 A113308

Adjacent sequences:  A101276 A101277 A101278 * A101280 A101281 A101282

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 22 2006; definition corrected May 23 2006

STATUS

approved

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Last modified January 20 02:57 EST 2019. Contains 319323 sequences. (Running on oeis4.)