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 A328010 The 5x + 1 sequence beginning at 17. 3
 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The 5x+1 problem is similar to the 3x+1 or Collatz problem. For some starting values it is known that the 5x+1 trajectory will tend to infinity or enter a periodic orbit. Alex V. Kontorovich & Jeffrey C. Lagarias conjectured that there are very few periodic orbits. One of them is shown here. The two other known periodic orbits are given in the crossrefs. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Alex V. Kontorovich & Jeffrey C. Lagarias, Stochastic Models for the 3x+1 and 5x+1 Problems arXiv:0910.1944 [math.NT], 2009. Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1). FORMULA a(n+1) = 5*a(n) + 1 if a(n) is odd, a(n+1) = a(n)/2 otherwise. From Colin Barker, Oct 04 2019: (Start) G.f.: (17 + 86*x + 43*x^2 + 216*x^3 + 108*x^4 + 54*x^5 + 27*x^6 + 136*x^7 + 68*x^8 + 34*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)). a(n) = a(n-10) for n>9. (End) PROG (PARI) Vec((17 + 86*x + 43*x^2 + 216*x^3 + 108*x^4 + 54*x^5 + 27*x^6 + 136*x^7 + 68*x^8 + 34*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Oct 05 2019 CROSSREFS Cf. A259207, A328011. Sequence in context: A288420 A156157 A146389 * A041554 A080770 A118863 Adjacent sequences: A328007 A328008 A328009 * A328011 A328012 A328013 KEYWORD nonn,easy AUTHOR Antoine Beaulieu, Oct 01 2019 STATUS approved

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Last modified June 7 21:25 EDT 2023. Contains 363157 sequences. (Running on oeis4.)