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A185454
Trajectory of 5 under repeated application of the map in A185452.
4
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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 04 2011
EXTENSIONS
Comment corrected by Paolo P. Lava, Mar 10 2011
STATUS
approved