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A008883 3x+1 sequence starting at 51.

%I A008883 #33 Jul 08 2025 01:22:29
%S A008883 51,154,77,232,116,58,29,88,44,22,11,34,17,52,26,13,40,20,10,5,16,8,4,
%T A008883 2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,
%U A008883 1,4,2,1,4,2,1,4,2,1,4,2,1
%N A008883 3x+1 sequence starting at 51.
%D A008883 R. K. Guy, Unsolved Problems in Number Theory, E16.
%H A008883 Vincenzo Librandi, <a href="/A008883/b008883.txt">Table of n, a(n) for n = 0..200</a>
%H A008883 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A008883 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%p A008883 f := proc(n) option remember; if n = 0 then 51; elif f(n-1) mod 2 = 0 then f(n-1)/2 else 3*f(n-1)+1; fi; end;
%t A008883 NestList[If[EvenQ[#], #/2, 3# + 1]&, 51, 100] (* _Vincenzo Librandi_, Jul 29 2014 *)
%o A008883 (Magma) [n eq 1 select 51 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 A008883 (PARI) Collatz(n,lim=0)={
%o A008883 my(c=n,e=0,L=List(n)); if(lim==0, e=1; lim=n*10^6);
%o A008883 for(i=1,lim, if(c%2==0, c=c/2, c=3*c+1); listput(L,c); if(e&&c==1, break));
%o A008883 return(Vec(L)); }
%o A008883 print(Collatz(51,60)) \\ A008883 (from 51 first 60)
%o A008883 \\ _Anatoly E. Voevudko_, Mar 26 2016
%Y A008883 Cf. similar sequences listed in A245671.
%Y A008883 Row 51 of A347270.
%K A008883 nonn,easy
%O A008883 0,1
%A A008883 _N. J. A. Sloane_