A008896 - OEIS

%I #16 Apr 25 2020 11:48:14

%S 66,33,98,49,146,73,218,109,326,163,488,244,122,61,182,91,272,136,68,

%T 34,17,50,25,74,37,110,55,164,82,41,122,61,182,91,272,136,68,34,17,50,

%U 25,74,37,110,55,164,82,41,122

%N 3x - 1 sequence starting at 66.

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

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

%F a(0) = 66, a(n) = a(n - 1)/2 if a(n - 1) is even, otherwise 3a(n - 1) - 1.

%t NestList[If[EvenQ[#], #/2, 3# - 1] &, 66, 50] (* or *) PadRight[ {66, 33, 98, 49, 146, 73, 218, 109, 326, 163, 488, 244}, 120, {68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82, 41, 122, 61, 182, 91, 272, 136}] (* _Harvey P. Dale_, Sep 02 2018 *)

%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.map(_ * -1) // _Alonso del Arte_, Apr 25 2020

%Y Cf. A008880 (3x + 1 sequence starting at 33).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More specific name from _Alonso del Arte_, Apr 25 2020 (was "x -> x/2 if x even, x -> 3x - 1 if x odd").