A170927 -id:A170927 - cp's OEIS frontend

A260239 Consider the 2^n values of A147562(i)/i^2 for 2^n <= i < 2^(n+1); a(n) = value of i where this quantity is minimized.

1, 3, 5, 11, 23, 45, 91, 183, 365, 731, 1461, 2923, 5847, 11693, 23387, 46775, 93549, 187099, 374197, 748395, 1496791, 2993581, 5987163, 11974327, 23948653, 47897307, 95794615, 191589229, 383178459, 766356917, 1532713835, 3065427671

Offset: 0

Steven Finch, Jul 20 2015

nonn

This sequence (for Ulam-Warburton) is analogous to A170927 (for toothpicks). Further, the lower limit of A147562(n)/n^2 evidently approaches twice the constant given in A195853.

Note that all values in this sequence are odd and that a(n)=2*a(n-1)+1 or a(n)=2*a(n-1)-1. - Robert Price, Aug 14 2015

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.

Robert Price, Table of n, a(n) for n = 0..291
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]

Cf. A139250, A147562, A170927, A195853.

A195853 Decimal expansion of the lower limit of A139250(i)/i^2.

Original entry on oeis.org

4, 5, 1, 3, 0, 5, 8, 2, 8, 4, 5, 3, 1, 2, 2, 1, 3, 5, 8, 9, 6, 4, 0, 1, 3, 4, 2, 2, 8, 0, 4, 0, 0, 1, 2, 3, 5, 1, 0, 2, 0, 4, 1, 3, 8, 3, 2, 9

Offset: 0

Omar E. Pol, Sep 27 2011

Constant mentioned in the Applegate-Pol-Sloane article, Section 5, the fractal-like structure. It is also mentioned in A139250 and A170927.
Note that at least there are 162 constants starting with 0.451305 in the Plouffe's Inverter.
Also evidently half the lower limit of A147562(n)/n^2; see A260239. - Steven Finch, Jul 21 2015

			0.451305...

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

Cf. A139250, A170927, A147562, A260239.

a(6)-a(14) from Robert Price, Aug 18 2012
a(15)-a(47) from Robert Price, Aug 16 2015
Removed first fifteen terms as they were duplicated in the last edit by Robert Price, Dec 17 2018

A261313 Decimal expansion of the lower limit of A147562(i)/i^2.

Original entry on oeis.org

9, 0, 2, 6, 1, 1, 6, 5, 6, 9, 0, 6, 2, 4, 4, 2, 7, 1, 7, 9, 2, 8, 0, 2, 6, 8, 4, 5, 6, 0, 8, 0, 0, 2, 4, 7, 0, 2, 0, 4, 0, 8, 2, 7, 6, 6, 5, 9, 9, 1, 6, 6, 0, 7, 9, 5, 1, 8, 2, 5, 8, 6, 7, 3, 9, 6, 6, 6, 2, 1, 5, 2, 5, 0, 4, 4, 3, 3, 8, 5, 2, 7, 6, 6, 3, 8, 3

Offset: 0

Robert Price, Aug 14 2015

Evidently twice the lower limit of A139250(n)/n^2 and thus twice A195853.

			0.90261165..

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

Cf. A139250, A170927, A147562, A195853, A260239.

Name and first 10 terms suggested by Steven Finch, Jul 21 2015

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

Robert Price, Sep 05 2015

Sequence suggested by Omar E. Pol.
Similar to the constant mentioned in the Applegate-Pol-Sloane article, Section 5, the fractal-like structure. It is also mentioned in A139250 and A170927.
It appears that this sequence is a quarter of A261313 and half of A195853.

			0.2256529142...

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

Cf. A139250, A147562, A162795, A170927, A195853, A260239, A261313, A261896.

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

Robert Price, Sep 05 2015

nonn

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).

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.

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]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Cf. A139250, A147562, A162795, A170927, A195853, A260239, A261313, A261895.

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

cp's OEIS Frontend

A260239 Consider the 2^n values of A147562(i)/i^2 for 2^n <= i < 2^(n+1); a(n) = value of i where this quantity is minimized.

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A195853 Decimal expansion of the lower limit of A139250(i)/i^2.

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A261313 Decimal expansion of the lower limit of A147562(i)/i^2.

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A261895 Decimal expansion of the lower limit of A162795(i)/i^2.

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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.

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