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 A095388 #15 May 18 2024 14:52:48
%S A095388 6,12,120,432,864,1728,3456,6912,931328,4357120,19789824,249753600,
%T A095388 499507200,1272561664,5226070016,10452140032,351882051584,
%U A095388 1215818366976,3364158439424,6953815244800,13907630489600,27815260979200,55630521958400,1343005923475456
%N A095388 Smallest multiple of 2^n whose Collatz (3x+1) trajectory includes at least one larger number.
%C A095388 Although the Collatz trajectory of a multiple of 2^n begins with n consecutive halving steps, some such trajectories nevertheless reach a larger peak value.
%e A095388 The Collatz trajectory of 120 = 2^3 * 15 begins with {120, 60, 30, 15, 46, 23, 70, 35, 106, 53, 160, ...}, and 160 > 120, and there is no number k < 120 of the form 2^3 * m whose trajectory includes a number > k, so a(3) = 120.
%t A095388 c[x_]:=c[x]=(1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1);c[1]=1; fpl[x_]:=Delete[FixedPointList[c, x], -1] {k=65536, ta=Table[0, {100}], u=1}; {$RecursionLimit=1000;m=0}; Do[If[Greater[Max[fpl[k*n]], k*n], Print[{k*n, n}]; ta[[u]]=k*n;u=u+1], {n, 1, 1000000}] [Code for 2^16 divisor, a(16)].
%Y A095388 Cf. A025586.
%K A095388 nonn
%O A095388 1,1
%A A095388 _Labos Elemer_, Jun 14 2004
%E A095388 a(17)-a(24) from _Donovan Johnson_, Feb 02 2011
%E A095388 Edited by _Jon E. Schoenfield_, May 18 2024