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

1,1

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.

Links

Table of n, a(n) for n=1..24.

Example

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.

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)].

Crossrefs

Cf. A025586.

Sequence in context: A144760 A207838 A191662 * A038515 A335735 A051586

Adjacent sequences: A095385 A095386 A095387 * A095389 A095390 A095391

Keyword

nonn

Author

Labos Elemer, Jun 14 2004

Extensions

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

Edited by Jon E. Schoenfield, May 18 2024

Status

approved