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3x+1 sequence starting at 57.
4

%I #26 Sep 08 2022 08:44:36

%S 57,172,86,43,130,65,196,98,49,148,74,37,112,56,28,14,7,22,11,34,17,

%T 52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,

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

%N 3x+1 sequence starting at 57.

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

%H Vincenzo Librandi, <a href="/A008877/b008877.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 57; 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]&, 57, 100] (* _Vincenzo Librandi_, Jul 29 2014 *)

%o (Haskell)

%o a008877 n = a008877_list !! n

%o a008877_list = 57 : iterate a006370 57

%o -- _Reinhard Zumkeller_, Aug 30 2012

%o (Magma) [n eq 1 select 57 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

%Y Cf. A006370.

%Y Row 57 of A347270.

%K nonn

%O 0,1

%A _N. J. A. Sloane_.