A135287 - OEIS

%I #16 Mar 02 2023 10:44:13

%S 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,

%T 44,22,11,43,76,38,19,55,92,46,23,63,104,52,26,13,58,29,76,38,19,69,

%U 120,60,30,15,70,35,92,46,23,83

%N 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.

%C 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.

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

%C The parameter C1 tells how many regular subclasses are there.

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

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

%C 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:

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

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

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

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

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

%H Reinhard Zumkeller, <a href="/A135287/b135287.txt">Table of n, a(n) for n = 0..10000</a>

%p 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

%t 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 *)

%o (Haskell)

%o a135287 n = a135287_list !! n

%o a135287_list = 1 : f 1 1 where

%o    f x y = z : f (x + 1) z where

%o         z = if m == 0 then y' else x + y; (y',m) = divMod y 2

%o -- _Reinhard Zumkeller_, Mar 02 2012

%Y Cf. A008336, A005132, A135294.

%Y Cf. A090895.

%K nonn,easy

%O 0,2

%A _Ctibor O. Zizka_, Dec 03 2007, Dec 05 2007

%E More terms from _R. J. Mathar_, Dec 12 2007

%E Offset fixed by _Reinhard Zumkeller_, Mar 02 2012