A135287 a(0)=1; for n > 0, a(n) = a(n-1)+n if a(n-1) is odd, else a(n) = a(n-1)/2.

1, 2, 1, 4, 2, 1, 7, 14, 7, 16, 8, 4, 2, 1, 15, 30, 15, 32, 16, 8, 4, 2, 1, 24, 12, 6, 3, 30, 15, 44, 22, 11, 43, 76, 38, 19, 55, 92, 46, 23, 63, 104, 52, 26, 13, 58, 29, 76, 38, 19, 69, 120, 60, 30, 15, 70, 35, 92, 46, 23, 83

Offset

0,2

Comments

Let a(0), C1, C2, C be integers. Consider the sequence a(n) = a(n-1) + C1*n + C2 if a(n-1) is not divisible by C or a(n) = a(n-1)/C otherwise.

For a fixed C1, C2, C this sequence shows chaotic behavior for some a(0) and a highly regular behavior for other a(0).

The parameter C1 tells how many regular subclasses are there.

The sequence grows roughly as a(n) ~ n*const.

Here C = 2. Other sequences showing very interesting behavior have C = power of 2.

Example: C1=3, C2=10, C=3. Thus a(n)= a(n-1)+3*n+10 if a(n-1) is not divisible by 3, or a(n)= a(n-1)/3 otherwise. There are 2 classes:

a regular class with 3 subclasses (C1=3) for initial values

{a(0)=3,38,79,...}

{a(0)=1,8,12,42,47,49,63,77,88,...}

{a(0)=2,43,45,...}

and a "chaotic" class for other initial values a(0).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Maple

A135287 := proc(n) option remember ; if n = 0 then 1 ; elif A135287(n-1) mod 2 = 0 then A135287(n-1)/2 ; else n+A135287(n-1) ; fi ; end: seq(A135287(n), n=0..60) ; # R. J. Mathar, Dec 12 2007

Mathematica

nxt[{n_, a_}]:={n+1, If[OddQ[a], a+n+1, a/2]}; NestList[nxt, {0, 1}, 60][[;; , 2]] (* Harvey P. Dale, Mar 02 2023 *)

Prog

(Haskell)
a135287 n = a135287_list !! n
a135287_list = 1 : f 1 1 where
   f x y = z : f (x + 1) z where
        z = if m == 0 then y' else x + y; (y', m) = divMod y 2
-- Reinhard Zumkeller, Mar 02 2012

Crossrefs

Cf. A008336, A005132, A135294.

Cf. A090895.

Sequence in context: A074586 A277812 A134586 * A359803 A290650 A346874

Adjacent sequences: A135284 A135285 A135286 * A135288 A135289 A135290

Keyword

nonn,easy

Author

Ctibor O. Zizka, Dec 03 2007, Dec 05 2007

Extensions

More terms from R. J. Mathar, Dec 12 2007

Offset fixed by Reinhard Zumkeller, Mar 02 2012

Status

approved