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%I #17 Apr 26 2020 17:48:32
%S 36,18,9,26,13,38,19,56,28,14,7,20,10,5,14,7,20,10,5,14,7,20,10,5,14,
%T 7,20,10,5,14,7,20,10,5,14,7,20,10,5,14,7,20,10,5,14,7,20,10,5,14,7,
%U 20,10,5,14,7,20,10,5,14,7,20
%N 3x - 1 sequence starting at 36.
%C Previous name was "x -> x/2 if x even, x -> 3x - 1 if x odd."
%D R. K. Guy, Unsolved Problems in Number Theory, E16.
%H Colin Barker, <a href="/A008894/b008894.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F a(0) = 36, a(n) = a(n - 1)/2 if a(n - 1) is even, otherwise 3a(n - 1) - 1.
%F From _Colin Barker_, Apr 26 2020: (Start)
%F G.f.: (36 + 18*x + 9*x^2 + 26*x^3 + 13*x^4 + 2*x^5 + x^6 + 47*x^7 + 2*x^8 + x^9 - 31*x^10 + x^11 - 46*x^12 - 23*x^13) / ((1 - x)*(1 + x + x^2 + x^3 + x^4)).
%F a(n) = a(n - 5) for n > 13.
%F (End)
%t -NestList[If[EvenQ[#], #/2, 3# + 1] &, -36, 100] (* _Alonso del Arte_, Apr 26 2020 *)
%o (Scala) def collatz(n: Int): Int = n % 2 match {
%o case 0 => n / 2
%o case _ => 3 * n + 1
%o }
%o def collatzSeq(n: Int): LazyList[Int] = LazyList.iterate(n)(collatz)
%o collatzSeq(-36).take(100).toList.map(_ * -1) // _Alonso del Arte_, Apr 26 2020
%o (PARI) Vec((36 + 18*x + 9*x^2 + 26*x^3 + 13*x^4 + 2*x^5 + x^6 + 47*x^7 + 2*x^8 + x^9 - 31*x^10 + x^11 - 46*x^12 - 23*x^13) / ((1 - x)*(1 + x + x^2 + x^3 + x^4)) + O(x^70)) \\ _Colin Barker_, Apr 26 2020
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
%E More specific name from _Alonso del Arte_, Apr 26 2020
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