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3x+1 sequence beginning at 9.
12

%I #29 Nov 17 2021 17:02:22

%S 9,28,14,7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,4,2,1,4,2,

%T 1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,

%U 4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1

%N 3x+1 sequence beginning at 9.

%H Colin Barker, <a href="/A033479/b033479.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

%F From _Colin Barker_, Oct 04 2019: (Start)

%F G.f.: (9 + 28*x + 14*x^2 - 2*x^3 - 6*x^4 - 3*x^5 + 27*x^6 - 5*x^7 + 41*x^8 - 8*x^9 - 4*x^10 - 12*x^11 - 6*x^12 - 3*x^13 - 35*x^14 - 4*x^15 - 2*x^16 - x^17 - 14*x^18 - 7*x^19) / ((1 - x)*(1 + x + x^2)).

%F a(n) = a(n-3) for n>19.

%F (End)

%e 9 is odd, so the next term is 3*9 + 1 = 28.

%e 28 is even, so the next term is 28/2 = 14.

%t NestList[If[EvenQ[#], #/2, 3# + 1] &, 9, 100] (* _Harvey P. Dale_, Dec 16 2012 *)

%o (Scala) def collatz(n: Int): Int = (n % 2) match {

%o case 0 => n / 2

%o case 1 => 3 * n + 1

%o }

%o import scala.collection.mutable.ListBuffer

%o val start = 9; var curr = start; var trajectory = new ListBuffer[Int]()

%o for (_ <- 1 to 100) {

%o trajectory += curr; curr = collatz(curr)

%o }

%o trajectory // _Alonso del Arte_, Jun 02 2019

%o (PARI) Vec((9 + 28*x + 14*x^2 - 2*x^3 - 6*x^4 - 3*x^5 + 27*x^6 - 5*x^7 + 41*x^8 - 8*x^9 - 4*x^10 - 12*x^11 - 6*x^12 - 3*x^13 - 35*x^14 - 4*x^15 - 2*x^16 - x^17 - 14*x^18 - 7*x^19) / ((1 - x)*(1 + x + x^2)) + O(x^80)) \\ _Colin Barker_, Oct 04 2019

%o (Python)

%o from itertools import accumulate

%o def f(x, _): return x//2 if x%2 == 0 else 3*x+1

%o print(list(accumulate([9]*92, f))) # _Michael S. Branicky_, Sep 28 2021

%Y Cf. A070165.

%Y Row 9 of A347270.

%K nonn,easy

%O 0,1

%A _Jeff Burch_