The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A060445 "Dropping time" in 3x+1 problem starting at 2n+1 (number of steps to reach a lower number than starting value). Also called glide(2n+1). 11
 0, 6, 3, 11, 3, 8, 3, 11, 3, 6, 3, 8, 3, 96, 3, 91, 3, 6, 3, 13, 3, 8, 3, 88, 3, 6, 3, 8, 3, 11, 3, 88, 3, 6, 3, 83, 3, 8, 3, 13, 3, 6, 3, 8, 3, 73, 3, 13, 3, 6, 3, 68, 3, 8, 3, 50, 3, 6, 3, 8, 3, 13, 3, 24, 3, 6, 3, 11, 3, 8, 3, 11, 3, 6, 3, 8, 3, 65, 3, 34, 3, 6, 3, 47, 3, 8, 3, 13, 3, 6, 3, 8, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS If the starting value is even then of course the next step in the trajectory is smaller (cf. A102419). The dropping time can be made arbitrarily large: If the starting value is of form n(2^m)-1 and m > 1, the next value is 3n(2^m)-3+1. That divided by 2 is 3n(2^(m-1))-1. It is bigger than the starting value and of the same form - substitute 3n -> n and m-1 -> m, so recursively get an increasing subsequence of m odd values. The dropping time is obviously longer than that. This holds even if Collatz conjecture were refuted. For example, m=5, n=3 -> 95, 286, 143, 430, 215, 646, 323, 970, 485, 1456, 728, 364, 182, 91. So the subsequence in reduced Collatz variant is 95, 143, 215, 323, 485. - Juhani Heino, Jul 21 2017 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 Jason Holt, Plot of first 1 billion terms, log scale on x axis Jason Holt, Plot of first 10 billion terms, log scale on x axis Eric Roosendaal, On the 3x + 1 problem EXAMPLE 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2, taking 6 steps, so a(1) = 6. MATHEMATICA nxt[n_]:=If[OddQ[n], 3n+1, n/2]; Join[{0}, Table[Length[NestWhileList[nxt, n, #>=n&]]-1, {n, 3, 191, 2}]]  (* Harvey P. Dale, Apr 23 2011 *) PROG (Haskell) a060445 0 = 0 a060445 n = length \$ takeWhile (>= n') \$ a070165_row n'             where n' = 2 * n + 1 -- Reinhard Zumkeller, Mar 11 2013 (Python) def a(n):     if n<1: return 0     n=2*n + 1     N=n     x=0     while True:         if n%2==0: n//=2         else: n = 3*n + 1         x+=1         if n

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)