A008894 - OEIS

%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