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A008908 Number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem, or -1 if 1 is never reached. 30
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

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

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 steps thus until reaching 1 leads to sequence A064433. [Michael Vielhaber (vielhaber(AT)gmail.com), Nov 18 2009]

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

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

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). - Reinhard Zumkeller, May 04 2009

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 xrange(1, 101)] # Indranil Ghosh, Apr 15 2017

CROSSREFS

Cf. A006577, A006370, A006667, A075677.

Sequence in context: A169844 A076123 A021783 * A050077 A261715 A185576

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

STATUS

approved

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Last modified June 26 13:33 EDT 2017. Contains 288766 sequences.