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A261896
Consider the 2^n values of A162795(i)/i^2 for 2^n <= i < 2^(n+1); a(n) = value of i where this quantity is minimized.
1
3, 5, 11, 25, 43, 89, 179, 361, 727, 1459, 2921, 5843, 11689, 23383, 46769, 93543, 187093, 374193, 748391, 1496785, 2993575, 5987157, 11974321, 23948647, 47897299, 95794607, 191589221, 383178449, 766356903, 1532713827, 3065427663, 6130855333, 12261710675, 24523421357, 49046842723
OFFSET
0,1
COMMENTS
Sequence suggested by Omar E. Pol.
Note that all values in this sequence are odd and that a(n) is approximately 2*a(n-1).
REFERENCES
D. Applegate, O. E. Pol and N. J. A. Sloane, The toothpick sequence and other sequences from cellular automata, Congressus Numerantium, v. 206 (2010) 157-191.
LINKS
D. Applegate, O. E. Pol and N. J. A. Sloane, The toothpick sequence and other sequences from cellular automata; also available at arXiv:1004.3036v2, [math.CO], 2010.
Steven R. Finch, Toothpicks and Live Cells, July 21, 2015. [Cached copy, with permission of the author]
MATHEMATICA
T = 1; t[0] = 0; t[1] = 1; lst = {1};
Do[twon = 2^n; Tmin = 1; imin = 1;
Do[If[i==twon, t[i]=twon,
t[i]=2*t[i-twon]+t[i-twon+1];
If[OddQ[i], T=T+t[i];
Ttest=T/(i*i)];
If[Ttest<Tmin, Tmin=Ttest; imin=i ]],
{i, twon, 2*twon - 1}];
AppendTo[lst, imin],
{n, 1, 15}];
lst
N[Tmin, 10]
KEYWORD
nonn
AUTHOR
Robert Price, Sep 05 2015
STATUS
approved