A095388 Smallest multiple of 2^n whose Collatz (3x+1) trajectory includes at least one larger number.

6, 12, 120, 432, 864, 1728, 3456, 6912, 931328, 4357120, 19789824, 249753600, 499507200, 1272561664, 5226070016, 10452140032, 351882051584, 1215818366976, 3364158439424, 6953815244800, 13907630489600, 27815260979200, 55630521958400, 1343005923475456

Offset: 1

Author

Labos Elemer, Jun 14 2004

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A025586.

Programs

Mathematica

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)].

Extensions

a(17)-a(24) from Donovan Johnson, Feb 02 2011

Edited by Jon E. Schoenfield, May 18 2024