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 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. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 * A290650 A346874 A348533 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

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Last modified January 29 15:28 EST 2023. Contains 359923 sequences. (Running on oeis4.)