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A153727
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Repeat (1,4,2): Trajectory of 3x+1 sequence starting at 1.
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8
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1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2
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OFFSET
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0,2
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COMMENTS
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The sequence is periodic with period 3.
Contribution from Klaus Brockhaus, May 23 2010: (Start)
Continued fraction expansion of (7+sqrt(229))/18.
Decimal expansion of 142/999. (End)
a(A008585(n)) = 1; a(A016777(n)) = 4; a(A016789(n)) = 2. [Reinhard Zumkeller, Oct 08 2011]
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REFERENCES
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C. A. Pickover, The Math Book, 2009; Collatz Conjecture, pp 374-375.
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LINKS
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Table of n, a(n) for n=0..104.
Eric Weisstein's World of Mathematics, CollatzProblem
Wikipedia, Collatz conjecture
Index entries for sequences related to 3x+1 (or Collatz) problem
Index to sequences with linear recurrences with constant coefficients, signature (0,0,1).
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FORMULA
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a(3n)=1, a(3n+1)=4, a(3n+2)=2. G.f.: (1+4*x+2*x^2)/(1-x^3).
a(n)=4^n mod 7. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2009]
a(n)=(1/9)*{10*(n mod 3)+13*[(n+1) mod 3]-2*[(n+2) mod 3]}, with n>=0 [From Paolo P. Lava, Jun 17 2009]
a(n) = A130196(n) * A131534(n). [From Reinhard Zumkeller, Nov 12 2009]
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PROG
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(Sage) [power_mod(2, -n, 7)for n in xrange(0, 105)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2009]
(Sage) [power_mod(4, n, 7)for n in xrange(0, 105)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2009]
(PARI) A153727(n)=[1, 4, 2][n%3+1] \\ - M. F. Hasler, Feb 10 2011
(Haskell)
a153727 n = a153727_list !! n
a153727_list = iterate a006370 1 -- Reinhard Zumkeller, Oct 08 2011
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CROSSREFS
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Cf. A178236 (decimal expansion of (7+sqrt(229))/18). Appears in A179133 (n>=1).
Cf. A006370.
Sequence in context: A082901 A136619 A132708 * A210937 A016506 A133455
Adjacent sequences: A153724 A153725 A153726 * A153728 A153729 A153730
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KEYWORD
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nonn,easy
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AUTHOR
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Philippe DELEHAM, Dec 30 2008
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STATUS
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approved
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