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A008898
Trajectory of 84 under the map x -> x/2 for x even, x -> 3x - 1 for x odd.
1
84, 42, 21, 62, 31, 92, 46, 23, 68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82, 41, 122, 61, 182, 91, 272, 136, 68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82, 41, 122, 61, 182, 91, 272, 136, 68, 34, 17, 50, 25, 74, 37, 110
OFFSET
0,1
COMMENTS
The sequence enters a repeating cycle of length 18, starting at n = 8. - Felix Fröhlich, Jul 10 2017
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, E16.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
From Colin Barker, Mar 27 2019: (Start)
G.f.: (84 + 42*x + 21*x^2 + 62*x^3 + 31*x^4 + 92*x^5 + 46*x^6 + 23*x^7 + 68*x^8 + 34*x^9 + 17*x^10 + 50*x^11 + 25*x^12 + 74*x^13 + 37*x^14 + 110*x^15 + 55*x^16 + 164*x^17 - 2*x^18 - x^19 + 101*x^20 - x^21 + 151*x^22 - x^23 + 226*x^24 + 113*x^25) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x^3 + x^6)*(1 + x^3 + x^6)).
a(n) = a(n-18) for n>25.
(End)
MATHEMATICA
NestList[If[EvenQ[#], #/2, 3# - 1] &, 84, 100] (* Alonso del Arte, Jul 05 2017 *)
PROG
(PARI) terms(n) = my(x=84, i=0); while(i < n, print1(x, ", "); if(x%2==0, x=x/2, x=3*x-1); i++)
/* Print initial 100 terms as follows */
terms(100) \\ Felix Fröhlich, Jul 10 2017
(PARI) Vec((84 + 42*x + 21*x^2 + 62*x^3 + 31*x^4 + 92*x^5 + 46*x^6 + 23*x^7 + 68*x^8 + 34*x^9 + 17*x^10 + 50*x^11 + 25*x^12 + 74*x^13 + 37*x^14 + 110*x^15 + 55*x^16 + 164*x^17 - 2*x^18 - x^19 + 101*x^20 - x^21 + 151*x^22 - x^23 + 226*x^24 + 113*x^25) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x^3 + x^6)*(1 + x^3 + x^6)) + O(x^60)) \\ Colin Barker, Mar 27 2019
CROSSREFS
Sequence in context: A304379 A317916 A066689 * A033404 A252723 A341304
KEYWORD
nonn,easy
EXTENSIONS
Name edited by Felix Fröhlich, Jul 10 2017
STATUS
approved