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

2, 2, 5, 6, 5, 2, 9, 1, 4, 2

Offset

0,1

Comments

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.

References

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

Links

Table of n, a(n) for n=0..9.

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

Example

0.2256529142...

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<imin, Tmin=Ttest; imin=i ]],
      {i, twon, 2*twon - 1}];
    AppendTo[lst, imin],
    {n, 1, 15}];
lst
N[Tmin, 10]

Crossrefs

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

Sequence in context: A250303 A368554 A301477 * A112573 A233740 A266595

Adjacent sequences: A261892 A261893 A261894 * A261896 A261897 A261898

Keyword

nonn,cons,hard,more

Author

Robert Price, Sep 05 2015

Status

approved