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

Author

N. J. A. Sloane, Feb 04 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A185452, A185453, 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(5,120);

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

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)

Extensions

Comment corrected by Paolo P. Lava, Mar 10 2011