A095383 Number of different initial values for 3x+1 trajectories started with initial values not exceeding 2^n and in which the peak values are larger than 2^n.
0, 1, 4, 6, 19, 31, 73, 144, 331, 672, 1468, 3024, 6065, 9592, 19701, 39630, 79625, 157569, 316139, 632655, 1264043, 2532963, 5060484, 10128862, 20270752, 40575156, 81134041, 162268825, 324627203, 649177198, 1298516271, 2596827906
Offset: 1
Keywords
Examples
n=4: between iv={1,2,...,16} {7,9,11,13,14,15} provides
peak values larger than 16, so a[4]=6.
Programs
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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}]
Extensions
a(22)-a(32) from Donovan Johnson, Feb 02 2011