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A185453
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Trajectory of 1 under repeated application of the map in A185452.
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3
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1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4
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OFFSET
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1,2
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COMMENTS
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Periodic with period length 5.
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REFERENCES
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J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 88.
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LINKS
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Table of n, a(n) for n=1..109.
Index entries for sequences related to 3x+1 (or Collatz) problem
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,1).
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FORMULA
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a(n)=(1/25)*{14*[(n-1) mod 5]+19*(n mod 5)+29*[(n+1) mod 5]-16*[(n+2) mod 5]-[(n+3) mod 5]}, Paolo P. Lava, Mar 10 2011
G.f. -x*(1+3*x+8*x^2+4*x^3+2*x^4) / ( (x-1)*(x^4+x^3+x^2+x+1) ). - R. J. Mathar, Mar 11 2011
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MAPLE
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f:=n->if n mod 2 = 0 then n/2 else (5*n+1)/2; fi;
T:=proc(n, M) global f; local t1, i; t1:=[n];
for i from 1 to M-1 do t1:=[op(t1), f(t1[nops(t1)])]; od: t1; end;
T(1, 120);
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MATHEMATICA
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NestList[If[EvenQ[#], #/2, (5#+1)/2]&, 1, 110] (* From Harvey P. Dale, June 24 2011 *)
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CROSSREFS
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Cf. A185452, A185454, A185455.
Sequence in context: A002017 A118582 A086179 * A021967 A093524 A200343
Adjacent sequences: A185450 A185451 A185452 * A185454 A185455 A185456
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Feb 04 2011
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STATUS
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approved
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