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A185454 Trajectory of 5 under repeated application of the map in A185452. 3
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 (list; graph; refs; listen; history; text; internal format)
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

a(n) = (1/49)*(355*(n mod 7) + 537*((n+1) mod 7) + 901*((n+2) mod 7) - 702*((n+3) mod 7) - 177*((n+4) mod 7) + 33*((n+5) mod 7) + 264*((n+6) mod 7)) - 21*(C(2*n,n) mod 2). - Paolo P. Lava, Mar 10 2011.

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

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Last modified February 19 13:20 EST 2018. Contains 299333 sequences. (Running on oeis4.)