A170927
Consider the 2^n values of A139250(i)/i^2 for 2^n <= i < 2^(n+1); a(n) = value of i where this quantity is minimized.
Original entry on oeis.org
1, 2, 5, 12, 21, 44, 89, 180, 362, 728, 1459, 2921, 5843, 11690, 23384, 46770, 93544, 187094, 374193, 748391, 1496786, 2993576, 5987158, 11974321, 23948647, 47897300, 95794608, 191589222, 383178450, 766356910, 1532713828, 3065427664, 6130855333, 12261710675
Offset: 0
The values of A139250(i)/i^2 for i = 1 .., 15 are 1.0, 0.7500000000, 0.7777777778, 0.6875000000, 0.6000000000, 0.6388888889, 0.7142857143, 0.6718750000, 0.5802469136, 0.5500000000, 0.5537190083, 0.5486111111, 0.5621301775, 0.6275510204, 0.6888888889, 0.6679687500. The minimal value for 4 <= i <= 7 is 0.6000000000 at i=5.
- Robert Price, Table of n, a(n) for n = 0..169
- David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
- Steven R. Finch, Toothpicks and Live Cells, July 21, 2015. [Cached copy, with permission of the author]
- N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
A261895
Decimal expansion of the lower limit of A162795(i)/i^2.
Original entry on oeis.org
2, 2, 5, 6, 5, 2, 9, 1, 4, 2
Offset: 0
- D. Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191
- David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.], which is 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]
- N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
-
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
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.
Original entry on oeis.org
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
- 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.
-
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
Showing 1-3 of 3 results.
Comments