A095388 - OEIS

%I #15 May 18 2024 14:52:48

%S 6,12,120,432,864,1728,3456,6912,931328,4357120,19789824,249753600,

%T 499507200,1272561664,5226070016,10452140032,351882051584,

%U 1215818366976,3364158439424,6953815244800,13907630489600,27815260979200,55630521958400,1343005923475456

%N Smallest multiple of 2^n whose Collatz (3x+1) trajectory includes at least one larger number.

%C 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 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 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 Cf. A025586.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 14 2004

%E a(17)-a(24) from _Donovan Johnson_, Feb 02 2011

%E Edited by _Jon E. Schoenfield_, May 18 2024