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 A254783 #23 Feb 16 2025 08:33:24
%S A254783 1,57,847,1694,3039,3388,3479,6078,6776,6958,13916,27832,55664,111328,
%T A254783 236107,246721,311257,493442,622514,986884,1245028,1328233,1973768,
%U A254783 2052521,2490056,2656466,3947536,4105042,4980112,8210084
%N A254783 Numbers n such that A033493(n)/n is an integer.
%C A254783 If A033493(n)/n = M is even, then 2*n is a member of the sequence and A033493(2*n)/(2*n) = M/2 + 1.
%C A254783 a(31) > 10^7. - _Derek Orr_, Mar 12 2015
%C A254783 Sum of reciprocals seems to converge quickly to 1.0208... - _Derek Orr_, Mar 12 2015
%H A254783 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CollatzProblem.html">CollatzProblem</a>
%H A254783 Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>
%H A254783 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%t A254783 a033493[n_] := Block[{f}, f[1] = 1; f[x_Integer?OddQ] := 3 x + 1; f[x_Integer?EvenQ] := x/2; -1 + Plus @@ FixedPointList[f, n]]; Select[Range[10^5], IntegerQ[a033493[#]/#] &] (* _Michael De Vlieger_, Feb 09 2015, after _Alonso del Arte_ at A033493 *)
%o A254783 (PARI) Tsum(n)=s=n;while(n!=1,if(n==Mod(0,2),n=n/2;s+=n);if(n==Mod(1,2)&&n!=1,n=3*n+1;s+=n));s
%o A254783 for(n=1,10^6,if(type(Tsum(n)/n)=="t_INT",print1(n,", ")))
%Y A254783 Cf. A033493.
%K A254783 nonn,more,hard
%O A254783 1,2
%A A254783 _Derek Orr_, Feb 07 2015