login
A095384
Number of different initial values for 3x+1 trajectories started with initial values not exceeding 2^n and in which the peak values are also not larger than 2^n.
5
1, 2, 3, 4, 10, 13, 33, 55, 112, 181, 352, 580, 1072, 2127, 6792, 13067, 25906, 51447, 104575, 208149, 415921, 833109, 1661341, 3328124, 6648354, 13283680, 26533708, 53083687, 106166631, 212243709, 424564626, 848967377, 1698139390, 3396064464, 6791623786
OFFSET
0,2
EXAMPLE
n=4: between iv={1,2,...,16} {2,8}U{3,5,6,10,12,16} provides peak values smaller than or equal with 16, so a(4) = 10 = A087256(4)+4
MAPLE
b:= proc(n) option remember; `if`(n=1, 1,
max(n, b(`if`(n::even, n/2, 3*n+1))))
end:
a:= proc(n) option remember; local t; t:=2^n;
add(`if`(b(i)<=t, 1, 0), i=1..t)
end:
seq(a(n), n=0..20); # Alois P. Heinz, Sep 26 2024
MATHEMATICA
c[x_]:=c[x]=(1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1); c[1]=1; fpl[x_]:=FixedPointList[c, x]; {$RecursionLimit=1000; m=0}; Table[Print[{xm-1, m}]; m=0; Do[If[ !Greater[Max[fpl[n]], 2^xm], m=m+1], {n, 1, 2^xm}], {xm, 1, 30}]
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Length[Select[Range[x=2^n], Max[Collatz[#]] <= x &]], {n, 0, 10}] (* T. D. Noe, Apr 29 2013 *)
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 14 2004
EXTENSIONS
a(21)-a(32) from Donovan Johnson, Feb 02 2011
a(0) from T. D. Noe, Apr 29 2013
a(33)-a(34) from Donovan Johnson, Jun 05 2013
STATUS
approved