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%I #31 Sep 08 2022 08:46:21
%S 13,-38,-19,58,29,-86,-43,130,65,-194,-97,292,146,73,-218,-109,328,
%T 164,82,41,-122,-61,184,92,46,23,-68,-34,-17,52,26,13,-38,-19,58,29,
%U -86,-43,130,65,-194,-97,292,146,73,-218,-109,328,164,82,41,-122,-61,184,92,46,23,-68,-34,-17
%N -3x + 1 sequence beginning at 13.
%C The 3x + 1 problem remains unsolved. But the -3x + 1 problem is easy to answer definitively: none of the thirty-one numbers in this sequence reach 1 because they form a cycle that does not include 1.
%F a(0) = 13; a(n) = (-3)*a(n - 1) + 1 if a(n - 1) is odd, a(n) = a(n - 1)/2 otherwise.
%e 13 is odd, so it's followed by (-3) * 13 + 1 = -39 + 1 = -38.
%e -38 is even, so it's followed by -38/2 = -19.
%t NestList[If[EvenQ[#], #/2, -3# + 1] &, 13, 100]
%o (Magma) [n eq 1 select 13 else IsOdd(Self(n-1)) select -3*Self(n-1)+1 else Self(n-1) div 2: n in [1..80]]; // _Vincenzo Librandi_, Jun 11 2018
%K sign,easy
%O 0,1
%A _Alonso del Arte_, May 26 2018
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