A008898 Trajectory of 84 under the map x -> x/2 for x even, x -> 3x - 1 for x odd.

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A008895 A008896 A008897 * A008899 A008900 A008901

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Name edited by Felix Fröhlich, Jul 10 2017

Status

approved