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A095388
Smallest multiple of 2^n whose Collatz (3x+1) trajectory includes at least one larger number.
0
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
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.
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
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

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Last modified September 20 18:47 EDT 2024. Contains 376075 sequences. (Running on oeis4.)