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3x + 1 sequence starting at 33.
6

%I #31 Sep 08 2022 08:44:36

%S 33,100,50,25,76,38,19,58,29,88,44,22,11,34,17,52,26,13,40,20,10,5,16,

%T 8,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,

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

%N 3x + 1 sequence starting at 33.

%D R. K. Guy, Unsolved Problems in Number Theory, E16.

%H Vincenzo Librandi, <a href="/A008880/b008880.txt">Table of n, a(n) for n = 0..200</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).

%p f := proc(n) option remember; if n = 0 then 33; elif f(n-1) mod 2 = 0 then f(n-1)/2 else 3*f(n-1)+1; fi; end;

%t NestList[If[EvenQ[#], #/2, 3# + 1] &, 33, 100] (* _Vincenzo Librandi_, Jul 29 2014 *)

%o (Magma) [n eq 1 select 33 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..80]]; // _Vincenzo Librandi_, Jul 29 2014

%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(33).take(100).toList // _Alonso del Arte_, Apr 25 2020

%Y Cf. similar sequences listed in A245671.

%Y Cf. A008896 (3x - 1 sequence starting at 66).

%Y Row 33 of A347270.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.