A090388 -id:A090388 - cp's OEIS frontend

A352672 Decimal expansion of r = (3/2)*(1+sqrt(3)).

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

Offset: 1

Clark Kimberling, Mar 26 2022

			4.098076211353315940291169512258808550414...

Cf. A090388, A104956, A352673, A352674, A352676.

Apart from leading digits the same as A176325 and A104956.

r = N[(3/2) (1 + Sqrt[3]), 200]
RealDigits[r][[1]]

Equals A104956 + 3/2. - Michel Marcus, Mar 28 2022

Equals (3/2) * A090388. - Bernard Schott, Mar 28 2022

A337301 Triangle read by rows in which row n lists the closest integers to diagonal lengths of regular n-gon with unit edge length, n >= 4.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 4, 4, 4, 3, 3, 2, 2, 3, 3, 4, 4, 4, 4, 3, 3, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 3, 2, 2, 3, 4, 4, 5, 5, 5, 5, 4, 4, 3, 2, 2, 3, 4, 4, 5, 5, 5, 5, 5, 4, 4, 3, 2

Offset: 4

Mohammed Yaseen, Aug 22 2020

			Triangle begins:
1;
2, 2;
2, 2, 2;
2, 2, 2, 2;
2, 2, 3, 2, 2;
2, 3, 3, 3, 3, 2;
2, 3, 3, 3, 3, 3, 2;
2, 3, 3, 4, 4, 3, 3, 2;
2, 3, 3, 4, 4, 4, 3, 3, 2;
2, 3, 3, 4, 4, 4, 4, 3, 3, 2;
2, 3, 4, 4, 4, 4, 4, 4, 4, 3, 2;
2, 3, 4, 4, 5, 5, 5, 5, 4, 4, 3, 2;
2, 3, 4, 4, 5, 5, 5, 5, 5, 4, 4, 3, 2;
...
Row n lists the closest integers to the length of the diagonals drawn from a fixed vertex of a regular n-gon with unit edge length, n >= 4.
The lengths of the diagonals drawn from vertex A of a regular 8-gon ABCDEFGH with unit edge length are:
AC = 1.84775...
AD = 2.41421...
AE = 2.61312...
AF = 2.41421...
AG = 1.84775...
So the row for n=8 is 2, 2, 3, 2, 2.

Cf. A064313.
Decimal expansion of diagonal lengths of regular n-gons with unit edge length:
n=4  A002193.
n=5  A001622.
n=6  A002194, A000038.
n=7  A160389, A231187.
n=8  A179260, A014176, A121601.
n=9  A332437.
n=10 A188593, A104457, A019970, A134945.
n=11 A231186.
n=12 A188887, A090388, A337402, A019973, A214726.

T[n_,k_]:=Round[Sin[(k+1)*Pi/n]/Sin[Pi/n]]; Flatten[Table[T[n,k],{n,4,16},{k,1,n-3}]] (* Stefano Spezia, Sep 07 2020 *)

T(n,k) = round(sin((k+1)*Pi/n)/sin(Pi/n)), n >= 4, 1 <= k <= n-3.

A343620 Decimal expansion of the Hausdorff dimension of 4 X 2 carpets with rows of 3 and 1 sub-parts.

Original entry on oeis.org

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

Offset: 1

Kevin Ryde, Aug 04 2021

Bedford (page 100 figure 34) gives this type of carpet as an example where the Hausdorff dimension differs from the capacity dimension (which is 3/2).
  +---+---+---+---+    Fractal carpet with each S
  |   | S | S | S |    a shrunken copy of the whole.
  +---+---+---+---+    Any 3 parts in one row and
  | S |   |   |   |    1 part in the other row.
  +---+---+---+---+

			1.4499843134764958489211625600623791...

Timothy Bedford, Crinkly Curves, Markov Partitions and Dimension, Ph.D. thesis, University of Warwick, 1984, chapter 4.
Curtis T. McMullen, Hausdorff Dimension of General Sierpinski Carpets, Nagoya Mathematical Journal, volume 96, number 19, 1984, pages 1-9, see page 1 dim(R) for the case n=4, m=2, t_0 = 1, t_1 = 3.

Cf. A346639 (3 X 2 carpets), A090388 (1+sqrt(3)).

RealDigits[Log2[1 + Sqrt[3]], 10, 100][[1]] (* Amiram Eldar, Aug 04 2021 *)

Equals log_2(1+sqrt(3)).

A344111 Decimal expansion of 4 + sqrt(3).

Original entry on oeis.org

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

Offset: 1

Wesley Ivan Hurt, May 10 2021

Decimal expansion of the surface area of a gyrobifastigium with regular faces and unit edge length.

Essentially the same sequence of digits as A176102, A165663, A160390, A090388, A019973 and A002194. - R. J. Mathar, May 16 2021

			5.73205080756887729...

Wikipedia, Gyrobifastigium

Cf. A002194, A019973, A090388, A160390, A165663.

RealDigits[4 + Sqrt[3], 10, 100] // Flatten

A379467 Decimal expansion of (1 + sqrt(3))/3.

Original entry on oeis.org

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

Offset: 0

Stefano Spezia, Dec 23 2024

			0.91068360252295909784248211383529078898093508460346...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.6, p. 504.

Cf. A002194, A090388.

Mathematica
```
RealDigits[(1+Sqrt[3])/3,10,100][[1]]
```

Equals A090388/3.

Minimal polynomial: 9*x^2 - 6*x - 2. - Stefano Spezia, Aug 03 2025

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A352672 Decimal expansion of r = (3/2)*(1+sqrt(3)).

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A337301 Triangle read by rows in which row n lists the closest integers to diagonal lengths of regular n-gon with unit edge length, n >= 4.

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A343620 Decimal expansion of the Hausdorff dimension of 4 X 2 carpets with rows of 3 and 1 sub-parts.

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A344111 Decimal expansion of 4 + sqrt(3).

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A379467 Decimal expansion of (1 + sqrt(3))/3.

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