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A008877 3x+1 sequence starting at 57.

%I A008877 #28 Jul 08 2025 01:22:02
%S A008877 57,172,86,43,130,65,196,98,49,148,74,37,112,56,28,14,7,22,11,34,17,
%T A008877 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 A008877 2,1,4,2,1,4,2,1,4,2,1,4,2,1
%N A008877 3x+1 sequence starting at 57.
%D A008877 R. K. Guy, Unsolved Problems in Number Theory, E16.
%H A008877 Vincenzo Librandi, <a href="/A008877/b008877.txt">Table of n, a(n) for n = 0..200</a>
%H A008877 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A008877 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%p A008877 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 A008877 NestList[If[EvenQ[#], #/2, 3# + 1]&, 57, 100] (* _Vincenzo Librandi_, Jul 29 2014 *)
%o A008877 (Haskell)
%o A008877 a008877 n = a008877_list !! n
%o A008877 a008877_list = 57 : iterate a006370 57
%o A008877 -- _Reinhard Zumkeller_, Aug 30 2012
%o A008877 (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 A008877 Cf. A006370.
%Y A008877 Row 57 of A347270.
%K A008877 nonn
%O A008877 0,1
%A A008877 _N. J. A. Sloane_