A169745 -id:A169745 - cp's OEIS frontend

A169746 First differences of A169745.

2, 3, 6, 7, 3, 2, 12, 4, 5, 3, 19, 3, 3, 3, 6, 6, 2, 6, 36, 10, 6, 6, 6, 6, 9, 2, 3, 7, 3, 2, 67, 3, 3, 3, 8, 3, 3, 4, 6, 6, 6, 12, 5, 3, 6, 13, 3, 2, 3, 3, 6, 12, 4, 5, 3, 132, 31, 3, 8, 9, 3, 4, 9, 3, 6, 6, 9, 3, 6, 15, 2, 3, 3, 3, 7, 2, 3, 9, 3, 4, 14, 10, 3, 3, 2, 6, 7, 3, 2, 19, 3, 3, 3, 6, 6, 2, 6, 259

Offset: 1

N. J. A. Sloane, May 03 2010

nonn

N. J. A. Sloane, Table of n, a(n) for n = 1..9709

Cf. A109671, A169745.

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).

Original entry on oeis.org

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

Eric Angelini, Apr 30 2010

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)?

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

A variant of A030067. Cf. A169741-A169745.

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

  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;

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 *)

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

A169743 Numbers k such that A109671(k) = 1.

Original entry on oeis.org

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 23, 32, 37, 40, 43, 44, 46, 47, 64, 71, 74, 79, 80, 86, 88, 89, 92, 94, 95, 128, 133, 139, 142, 145, 148, 151, 158, 160, 163, 172, 175, 176, 178, 179, 184, 188, 190, 191, 256, 263, 266, 278, 283, 284, 290, 295, 296, 302, 307, 316, 319, 320

Offset: 1

N. J. A. Sloane, May 02 2010

nonn

If m is a term so is 2m.

Cf. A109671, A169744, A169745.

A169744 Odd numbers n such that A109671(n) = 1.

Original entry on oeis.org

1, 5, 11, 23, 37, 43, 47, 71, 79, 89, 95, 133, 139, 145, 151, 163, 175, 179, 191, 263, 283, 295, 307, 319, 331, 349, 353, 359, 373, 379, 383, 517, 523, 529, 535, 551, 557, 563, 571, 583, 595, 607, 631, 641, 647, 659, 685, 691, 695, 701, 707, 719, 743, 751, 761, 767, 1031, 1093

Offset: 1

N. J. A. Sloane, May 02 2010

nonn

Cf. A109671, A169743, A169745.

cp's OEIS Frontend

A169746 First differences of A169745.

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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).

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A169743 Numbers k such that A109671(k) = 1.

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A169744 Odd numbers n such that A109671(n) = 1.

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Author

Keywords

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