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A102419 "Dropping time" in 3x+1 problem starting at n (number of steps to reach a lower number than starting value); a(1) = 0 by convention. Also called glide(n). 7
0, 1, 6, 1, 3, 1, 11, 1, 3, 1, 8, 1, 3, 1, 11, 1, 3, 1, 6, 1, 3, 1, 8, 1, 3, 1, 96, 1, 3, 1, 91, 1, 3, 1, 6, 1, 3, 1, 13, 1, 3, 1, 8, 1, 3, 1, 88, 1, 3, 1, 6, 1, 3, 1, 8, 1, 3, 1, 11, 1, 3, 1, 88, 1, 3, 1, 6, 1, 3, 1, 83, 1, 3, 1, 8, 1, 3, 1, 13, 1, 3, 1, 6, 1, 3, 1, 8, 1, 3, 1, 73, 1, 3, 1, 13, 1, 3, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(2n) = 1; a(2n+1) = A060445(n).

a(n) = A074473(n)-1 for n>1.

a(n) = floor(A126241(n)*(1+log(2)/log(3))). [K. Spage, Oct 22 2009]

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Eric Roosendaal, On the 3x + 1 problem

N. J. A. Sloane, First 36 terms of A217934 and A060412 [From Roosendaal web site]

EXAMPLE

1: 0 steps

2 1: 1 step

3 10 5 16 8 4 2 1: 6 steps (before it drops below n)

4 2 1: 1 step

5 16 8 4 2 1: 3 steps

6 3 ...: 1 step

7 22 11 34 17 52 26 13 40 20 10 5 ...: 11 steps

...

Records: 0.1.6.11.96.132...171... (A217934)

at.......1.2.3..7.27.703.10087... (A060412)

MATHEMATICA

Prepend[Table[Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>=n&]], {n, 2, 99}], 1]-1 (* Jayanta Basu, May 28 2013 *)

PROG

(Python)

def a(n):

    if n<3: return n - 1

    N=n

    x=0

    while True:

        if n%2==0: n/=2

        else: n = 3*n + 1

        x+=1

        if n<N: return x

print [a(n) for n in xrange(1, 101)] # Indranil Ghosh, Apr 22 2017

CROSSREFS

Cf. A060445, A074473, A126241.

For records see A060412, A217934. - N. J. A. Sloane, Oct 20 2012

Sequence in context: A152935 A253686 A290101 * A074193 A074453 A069608

Adjacent sequences:  A102416 A102417 A102418 * A102420 A102421 A102422

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 15 2006

STATUS

approved

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Last modified September 21 15:31 EDT 2017. Contains 292310 sequences.