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A090895 a(1)=1 then a(n)=a(n-1)/2 if a(n-1) is even, a(n)=a(n-1)+n otherwise. 5
1, 3, 6, 3, 8, 4, 2, 1, 10, 5, 16, 8, 4, 2, 1, 17, 34, 17, 36, 18, 9, 31, 54, 27, 52, 26, 13, 41, 70, 35, 66, 33, 66, 33, 68, 34, 17, 55, 94, 47, 88, 44, 22, 11, 56, 28, 14, 7, 56, 28, 14, 7, 60, 30, 15, 71, 128, 64, 32, 16, 8, 4, 2, 1, 66, 33, 100, 50, 25, 95, 166, 83, 156, 78, 39 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Does a(n)=1 for infinitely many values of n ?

It seems that the answer is yes (see A185038). The number a(n) is always in the range on 1 to 3*a(n), and there is an average of 2 addition steps for every 5 steps. In order to reach '1', the sequence must reach a power of two after an addition step, which is likely to happen on an exponential basis. [Sergio Pimentel, Mar 01 2012]

a(A208852(n)) = n and a(m) != n for m < A208852(n); A185038(a(n)) = 1. [Reinhard Zumkeller, Mar 02 2012]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

sum(k=1, n, a(k)) seems to be asymptotic to c*n^2 where c=0.57....

MATHEMATICA

nxt[{n_, a_}]:={n+1, If[EvenQ[a], a/2, a+n+1]}; Transpose[NestList[nxt, {1, 1}, 80]][[2]] (* Harvey P. Dale, Aug 25 2015 *)

PROG

(PARI) a(n)=if(n<2, 1, if(a(n-1)%2, a(n-1)+n, a(n-1)/2))

(Haskell)

a090895 n = a090895_list !! (n-1)

a090895_list = 1 : f 2 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. A135287, A185038.

Sequence in context: A201143 A326935 A135003 * A337903 A264767 A065231

Adjacent sequences:  A090892 A090893 A090894 * A090896 A090897 A090898

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 25 2004

STATUS

approved

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Last modified April 18 10:21 EDT 2021. Contains 343087 sequences. (Running on oeis4.)