A185453 Trajectory of 1 under repeated application of the map in A185452.

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

Offset

1,2

Comments

Periodic with period length 5.

References

J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 88.

Links

Table of n, a(n) for n=1..109.

Index entries for sequences related to 3x+1 (or Collatz) problem

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Formula

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

Maple

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);

Mathematica

NestList[If[EvenQ[#], #/2, (5#+1)/2]&, 1, 110] (* Harvey P. Dale, Jun 24 2011 *)

Crossrefs

Cf. A185452, A185454, A185455.

Sequence in context: A118582 A356580 A086179 * A021967 A093524 A200343

Adjacent sequences: A185450 A185451 A185452 * A185454 A185455 A185456

Keyword

nonn

Author

N. J. A. Sloane, Feb 04 2011

Status

approved