login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008908 (1 + number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem), or -1 if 1 is never reached. 31
1, 2, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 10, 18, 18, 5, 13, 21, 21, 8, 8, 16, 16, 11, 24, 11, 112, 19, 19, 19, 107, 6, 27, 14, 14, 22, 22, 22, 35, 9, 110, 9, 30, 17, 17, 17, 105, 12, 25, 25, 25, 12, 12, 113, 113, 20, 33, 20, 33, 20, 20, 108, 108, 7, 28, 28, 28, 15, 15, 15, 103 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The number of steps (iterations of the map A006370) to reach 1 is given by A006577, this sequence counts 1 more. - M. F. Hasler, Nov 05 2017

When Collatz 3N+1 function is seen as an isometry over the dyadics, the halving step necessarily following each tripling is not counted, hence N -> N/2, if even, but N -> (3N+1)/2, if odd. Counting iterations of this map until reaching 1 leads to sequence A064433. [Michael Vielhaber (vielhaber(AT)gmail.com), Nov 18 2009]

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E16.

LINKS

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

J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.

Nitrxgen, Collatz Calculator

Wikipedia, Collatz conjecture

Index entries for sequences related to 3x+1 (or Collatz) problem

FORMULA

a(n) = A006577(n) + 1.

a(n) = f(n,1) with f(n,x) = if n=1 then x else f(A006370(n),x+1).

a(A033496(n)) = A159999(A033496(n)). - Reinhard Zumkeller, May 04 2009

a(n) = A006666(n) + A078719(n).

a(n) = length of n-th row in A070165. - Reinhard Zumkeller, May 11 2013

MATHEMATICA

Table[Length[NestWhileList[If[EvenQ[ # ], #/2, 3 # + 1] &, i, # != 1 &]], {i, 75}]

PROG

(Haskell)

a008908 = length . a070165_row

-- Reinhard Zumkeller, May 11 2013, Aug 30, Jul 19 2011

(PARI) a(n)=my(c=1); while(n>1, n=if(n%2, 3*n+1, n/2); c++); c \\ Charles R Greathouse IV, May 18 2015

(Python)

def a(n):

    if n==1: return 1

    x=1

    while True:

        if n%2==0: n/=2

        else: n = 3*n + 1

        x+=1

        if n<2: break

    return x

print [a(n) for n in range(1, 101)] # Indranil Ghosh, Apr 15 2017

CROSSREFS

Cf. A006577, A006370, A006667, A075677.

Sequence in context: A169844 A076123 A021783 * A050077 A261715 A309640

Adjacent sequences:  A008905 A008906 A008907 * A008909 A008910 A008911

KEYWORD

nonn,nice,look

AUTHOR

N. J. A. Sloane, Bill Gosper

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001

"Escape clause" added to definition by N. J. A. Sloane, Jun 06 2017

Edited by M. F. Hasler, Nov 05 2017

STATUS

approved

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 23 19:36 EST 2020. Contains 331175 sequences. (Running on oeis4.)