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A066861 For x > 0 let f(x) = x/2 if x is even, f(x) = (3*x+1)/2 if x is odd (3x+1 or Collatz problem). Sequence gives numbers such that k-1 applications of f lead to k for some k > 0. 1

%I

%S 1,3,4,10,11,12,18,19,24,26,32,34,35,43,49,56,58,60,61,65,66,67,80,96,

%T 104,106,113,121,130,131,132,133,134,144,145,146,147,148,149,153,156,

%U 157,158,167,169,176,180,181,184,186,192,196,197,198,200,202,204,205,206,207,222,223,246,247,249,254,255

%N For x > 0 let f(x) = x/2 if x is even, f(x) = (3*x+1)/2 if x is odd (3x+1 or Collatz problem). Sequence gives numbers such that k-1 applications of f lead to k for some k > 0.

%C Conjecture: a(n) = n*log(n) asymptotically.

%C Numbers n such that A258769(n)> 0. - _Derek Orr_, Jun 11 2015

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F f^(k-1)(n) = k.

%e 11 is in the sequence since seven applications of f lead to 8: 11 -> 17 -> 26 -> 13 -> 20 -> 10 -> 5 -> 8; 145 is in the sequence since 60 applications of f lead to 61.

%o (PARI) {for(n=1,205,k=1; x=n; while(x!=1&&x!=k,x=if(x%2==0, x/2,(3*x+1)/2); k++); if(x==k,print1(n,",")))}

%Y Cf. A014682, A258769.

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Jan 22 2002

%E Edited by _Klaus Brockhaus_, May 26 2003

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Last modified May 25 11:27 EDT 2020. Contains 334592 sequences. (Running on oeis4.)