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A008880 3x + 1 sequence starting at 33.

%I A008880 #33 Jul 08 2025 01:22:18
%S A008880 33,100,50,25,76,38,19,58,29,88,44,22,11,34,17,52,26,13,40,20,10,5,16,
%T A008880 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 A008880 4,2,1,4,2,1,4,2,1,4,2,1,4
%N A008880 3x + 1 sequence starting at 33.
%D A008880 R. K. Guy, Unsolved Problems in Number Theory, E16.
%H A008880 Vincenzo Librandi, <a href="/A008880/b008880.txt">Table of n, a(n) for n = 0..200</a>
%H A008880 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A008880 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%p A008880 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 A008880 NestList[If[EvenQ[#], #/2, 3# + 1] &, 33, 100] (* _Vincenzo Librandi_, Jul 29 2014 *)
%o A008880 (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 A008880 (Scala) def collatz(n: Int): Int = n % 2 match {
%o A008880   case 0 => n / 2
%o A008880   case _ => 3 * n + 1
%o A008880 }
%o A008880 def collatzSeq(n: Int): LazyList[Int] = LazyList.iterate(n)(collatz)
%o A008880 collatzSeq(33).take(100).toList // _Alonso del Arte_, Apr 25 2020
%Y A008880 Cf. similar sequences listed in A245671.
%Y A008880 Cf. A008896 (3x - 1 sequence starting at 66).
%Y A008880 Row 33 of A347270.
%K A008880 nonn,easy
%O A008880 0,1
%A A008880 _N. J. A. Sloane_