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A006667
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Number of tripling steps to reach 1 from n in '3x+1' problem, or -1 if 1 is never reached.
(Formerly M0019)
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57
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0, 0, 2, 0, 1, 2, 5, 0, 6, 1, 4, 2, 2, 5, 5, 0, 3, 6, 6, 1, 1, 4, 4, 2, 7, 2, 41, 5, 5, 5, 39, 0, 8, 3, 3, 6, 6, 6, 11, 1, 40, 1, 9, 4, 4, 4, 38, 2, 7, 7, 7, 2, 2, 41, 41, 5, 10, 5, 10, 5, 5, 39, 39, 0, 8, 8, 8, 3, 3, 3, 37, 6, 42, 6, 3, 6, 6, 11, 11, 1, 6, 40, 40, 1, 1, 9, 9, 4, 9, 4, 33, 4, 4, 38
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OFFSET
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1,3
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COMMENTS
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A075680, which gives the values for odd n, isolates the essential behavior of this sequence. - T. D. Noe, Jun 01 2006
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 204, Problem 22.
R. K. Guy, Unsolved Problems in Number Theory, E16.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(1) = 0, a(n) = a(n/2) if n is even, a(n) = a(3n+1)+1 if n>1 is odd. The Collatz conjecture is that this defines a(n) for all n >= 1.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 0,
`if`(n::even, a(n/2), 1+a(3*n+1)))
end:
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MATHEMATICA
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Table[Count[Differences[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]], _?Positive], {n, 100}] (* Harvey P. Dale, Nov 14 2011 *)
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PROG
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(PARI) for(n=2, 100, s=n; t=0; while(s!=1, if(s%2==0, s=s/2, s=(3*s+1)/2; t++); if(s==1, print1(t, ", "); ); ))
(Haskell)
a006667 = length . filter odd . takeWhile (> 2) . (iterate a006370)
a006667_list = map a006667 [1..]
(Python)
def a(n):
if n==1: return 0
x=0
while True:
if n%2==0: n/=2
else:
n = 3*n + 1
x+=1
if n<2: break
return x
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001
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STATUS
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approved
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