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A008908
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(1 + number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem), or -1 if 1 is never reached.
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36
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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;
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history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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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]
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, E16.
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LINKS
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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
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FORMULA
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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
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MAPLE
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a:= proc(n) option remember; 1+`if`(n=1, 0,
a(`if`(n::even, n/2, 3*n+1)))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Jan 29 2021
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MATHEMATICA
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Table[Length[NestWhileList[If[EvenQ[ # ], #/2, 3 # + 1] &, i, # != 1 &]], {i, 75}]
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PROG
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(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
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CROSSREFS
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Cf. A006577, A006370, A006667, A075677.
Sequence in context: A169844 A076123 A021783 * A050077 A261715 A309640
Adjacent sequences: A008905 A008906 A008907 * A008909 A008910 A008911
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KEYWORD
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nonn,nice,look
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AUTHOR
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N. J. A. Sloane, Bill Gosper
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EXTENSIONS
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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
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STATUS
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approved
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