A185454 Trajectory of 5 under repeated application of the map in A185452.

5, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, 52

Offset

1,1

Comments

Periodic with period length 7.

References

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

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

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

Formula

From Colin Barker, Feb 01 2018: (Start)

G.f.: x*(5 + 13*x + 33*x^2 + 83*x^3 + 208*x^4 + 104*x^5 + 52*x^6 + 21*x^7) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

a(n) = a(n-7) for n>8. (End)

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(5, 120);

Prog

(PARI) Vec(x*(5 + 13*x + 33*x^2 + 83*x^3 + 208*x^4 + 104*x^5 + 52*x^6 + 21*x^7) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^60)) \\ Colin Barker, Feb 01 2018

Crossrefs

Cf. A185452, A185453, A185455.

Sequence in context: A001981 A141025 A100227 * A278764 A183774 A027051

Adjacent sequences: A185451 A185452 A185453 * A185455 A185456 A185457

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 04 2011

Extensions

Comment corrected by Paolo P. Lava, Mar 10 2011

Status

approved