A109671 a(1)=1; thereafter, a(2n)=a(n), a(2n+1) is the smallest positive number such that |a(2n+1)-a(2n-1)|=a(n).

1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 3, 6, 1, 5, 2, 3, 1, 2, 1, 1, 2, 3, 3, 6, 3, 3, 6, 9, 1, 8, 5, 3, 2, 1, 3, 4, 1, 3, 2, 1, 1, 2, 1, 1, 2, 3, 3, 6, 3, 3, 6, 9, 3, 6, 3, 3, 6, 9, 9, 18, 1, 17, 8, 9, 5, 4, 3, 1, 2, 3, 1, 2, 3, 5, 4, 1, 1, 2, 3, 5, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 3, 6, 3, 3, 6, 9, 3

Offset: 1

Author

Eric Angelini, Apr 30 2010

Keywords

• nonn
• nice

Comments

A variant of the semi-Fibonacci numbers A030067.

Self-describing: the sequence of the absolute differences between odd-indexed terms is the sequence itself.

It appears that the record values form sequence A038754 and occur at indices of the form 2^k-1. - N. J. A. Sloane, May 02 2010

Does the sequence contain every positive integer (cf. A169741)?

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Crossrefs

A variant of A030067. Cf. A169741-A169745.

Programs

Haskell

import Data.List (transpose)
a109671 n = a109671_list !! (n-1)
a109671_list = concat (transpose [1 : f 1 a109671_list, a109671_list])
   where f u (v:vs) = y : f y vs where
           y = if u > v then u - v else u + v
-- Reinhard Zumkeller, Jul 07 2013

Maple

  f:=proc(n) option remember; local t1;
    if n = 1 then 1
    elif n mod 2 = 0 then f(n/2)
    else t1:= f(n-2)-f((n-1)/2);
 if t1 > 0 then t1 else f(n-2)+f((n-1)/2) fi fi end;

Mathematica

a[1] = 1; a[n_?EvenQ] := a[n/2]; a[n_] := a[n] = If[t1 = a[n-2] - a[(n-1)/2]; t1 > 0, t1, a[n-2] + a[(n-1)/2]]; Table[a[n], {n, 1, 104}] (* Jean-François Alcover, Nov 27 2012, after Maple *)

Extensions

Edited by N. J. A. Sloane, May 02 2010