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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 (list; graph; refs; listen; history; text; internal format)
 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 A128873 Adjacent sequences:  A008895 A008896 A008897 * A008899 A008900 A008901 KEYWORD nonn,easy AUTHOR EXTENSIONS Name edited by Felix Fröhlich, Jul 10 2017 STATUS approved

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Last modified September 28 05:33 EDT 2020. Contains 337392 sequences. (Running on oeis4.)