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

Author

N. J. A. Sloane, Feb 04 2011

Keywords

• nonn

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

• 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).

Crossrefs

Cf. A185452, A185454, A185455.

Programs

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 *)

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