This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080842 #15 Dec 23 2021 02:20:37
%S A080842 1,3,1,1,5,6,2,3,1,6,2,3,1,2,3,1,8,9,3,1,9,3,1,3,1,11,12,4,5,6,2,3,1,
%T A080842 12,4,5,6,2,3,1,4,5,6,2,3,1,14,15,5,6,2,3,1,15,5,6,2,3,1,5,6,2,3,1,17,
%U A080842 18,6,2,3,1,18,6,2,3,1,6,2,3,1,20,21,7,8,9,3,1,21,7,8,9,3,1,7,8,9,3,1,23,24
%N A080842 Numbers in the x/3 + 1 conjecture: Repeat until 1 is reached: if x is divisible by 3 then divide by 3, otherwise add 1.
%C A080842 These numbers converge to various last-3-digit endings and only two last-2-digit numbers: 2,1 or 3,1.
%e A080842 The trajectories starting at x=2, 3, 4 etc. are (3,1), (1), (5,6,2,3,1), (6,2,3,1), (2,3,1), (8,9,3,1) etc. Each "1" marks the end of a trajectory.
%t A080842 Join[{1},Flatten[Table[Rest[NestWhileList[If[Divisible[#,3],#/3,#+1]&,n, #!=1&]],{n,2,30}]]] (* _Harvey P. Dale_, Feb 02 2012 *)
%o A080842 (PARI) mult3p1(n, p) = { print1(1" "); for(j=1, n, x=j; while(x>1, if(x%3==0, x/=3, x = x*p+1 ) ; print1(x" ") ; ); ) ; print1(" ") ; } { mult3p1(30,1) ; } - _R. J. Mathar_, Feb 01 2008
%Y A080842 Cf. A080828, A067433.
%K A080842 easy,nonn,tabf
%O A080842 1,2
%A A080842 _Cino Hilliard_, Mar 28 2003
%E A080842 Edited and corrected by _R. J. Mathar_, Feb 01 2008