A120011 -id:A120011 - cp's OEIS frontend

A178818 Decimal expansion of the diameter of the regular 7-gon (heptagon) of edge length 1.

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 16 2010

			2.07652139657233656716353886148584033070572020662596852408341737686302...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for algebraic numbers, degree 6.

Cf. A090488, A102771, A104956, A120011, A178809, A178816, A178817.

SetDefaultRealField(RealField(100)); R:=RealField(); Cot(Pi(R)/7); // G. C. Greubel, Jan 22 2019

evalf[120](cot(Pi/7)); # Muniru A Asiru, Jan 22 2019

Mathematica
```
RealDigits[Cot[Pi/7],10, 100][[1]]
```

default(realprecision, 100); cotan(Pi/7) \\ G. C. Greubel, Jan 22 2019

numerical_approx(cot(pi/7), digits=100) # G. C. Greubel, Jan 22 2019

Digits of cot(Pi/7).

Largest of the 6 real-valued roots of 7*x^6 -35*x^4 +21*x^2 -1=0. - R. J. Mathar, Aug 29 2025

A385506 Decimal expansion of the volume of a triaugmented triangular prism with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 01 2025

The triaugmented triangular prism is Johnson solid J_51.

			1.140119483078766847782705947481317131020537251141...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Triaugmented triangular prism.

Cf. A097715 (surface area).

Cf. A002194, A010466, A010503, A120011, A385505.

First[RealDigits[(Sqrt[8] + Sqrt[3])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J51", "Volume"], 10, 100]]

Equals 1/sqrt(2) + sqrt(3)/4 = A010503 + A120011 = (A010466 + A002194)/4.

Equals the largest root of 256*x^4 - 352*x^2 + 25.

A364895 Decimal expansion of the 4-volume of the unit regular pentachoron (5-cell).

Original entry on oeis.org

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

Offset: 0

Jianing Song, Aug 12 2023

Decimal expansion of sqrt(5)/96.

In general, the n-volume of the unit regular n-simplex is sqrt(n+1)/(n!*2^(n/2)).

			Equals 0.02329237476562280933...

Wikipedia, 5-cell
Polytope Wiki, Pentachoron

Decimal expansion of 4-volumes: this sequence (5-cell), A000007 = 1 (8-cell or tesseract), A020793 = 1/6 (16-cell), A000038 = 2 (24-cell), A364896 (120-cell), A364897 (600-cell).

Decimal expansion of the n-volume of the unit regular n-simplex: A120011 (n=2), A020829 (n=3), this sequence (n=4).

First[RealDigits[Sqrt[5]/96, 10, 100, -1]] (* Paolo Xausa, Jun 12 2024 *)

PARI
```
sqrt(5)/96
```

A343486 Decimal expansion of (29/96)*sqrt(3).

Original entry on oeis.org

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

Offset: 0

Kevin Ryde, Apr 17 2021

Area of the convex hull around the terdragon fractal. As the limit of finite expansion levels, equals lim_{n->oo} (sqrt(3)/4) * A343485(n) / 3^n, where sqrt(3)/4 = A120011 is the area of a unit-side equilateral triangle.

			0.52322368145309834908641608232989894...

Kevin Ryde, Table of n, a(n) for n = 0..10000
Kevin Ryde, Iterations of the Terdragon Curve, see index "HAf".

Cf. A343485 (terdragon finite hull areas), A343487 (terdragon hull perimeter), A120011 (unit triangle area).

RealDigits[29*Sqrt[3]/96, 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)

my(c=29/96*quadgen(3*4)); a_vector(len) = digits(floor(c*10^len));

A386001 Decimal expansion of the surface area of a tridiminished icosahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 17 2025

The tridiminished icosahedron is Johnson solid J_63.

			7.32649571122799738518634385904816925690062907729...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Tridiminished icosahedron.

Cf. A386000 (volume).

Cf. A002194, A010476, A102771, A120011, A386003.

First[RealDigits[(5*Sqrt[3] + 3*Sqrt[25 + 10*Sqrt[5]])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J63", "SurfaceArea"], 10, 100]]

Equals (5*sqrt(3) + 3*sqrt(5*(5 + 2*sqrt(5))))/4 = (5*A002194 + 3*sqrt(5*(5 + A010476)))/4.
Equals 3*A102771 + 5*A120011 = A386003 - 2*A120011.
Equals the largest root of 256*x^8 - 19200*x^6 + 324000*x^4 - 1687500*x^2 + 1265625.

A386003 Decimal expansion of the surface area of an augmented tridiminished icosahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 18 2025

The augmented tridiminished icosahedron is Johnson solid J_64.

			8.192521115012436031950067029801105440372031704...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Augmented tridiminished icosahedron.

Cf. A386002 (volume).

Cf. A002194, A010476, A102771, A120011, A386001.

First[RealDigits[(7*Sqrt[3] + 3*Sqrt[25 + 10*Sqrt[5]])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J64", "SurfaceArea"], 10, 100]]

Equals (7*sqrt(3) + 3*sqrt(5*(5 + 2*sqrt(5))))/4 = (7*A002194 + 3*sqrt(5*(5 + A010476)))/4.
Equals 3*A102771 + 7*A120011 = A386001 + 2*A120011.
Equals the largest root of 256*x^8 - 23808*x^6 + 484704*x^4 - 2752812*x^2 + 4626801.

A154605 Decimal expansion of 2/(4th root of 3).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, Jan 12 2009

The side length of an equilateral triangle with area 1.

Quartic number with denominator 3 and minimal polynomial 3x^4 - 16. - Charles R Greathouse IV, Jun 30 2021

			1.5196713713031850946623755013090906...

Cf. A011002, A120011.

RealDigits[N[2/3^(1/4),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2012 *)
RealDigits[2/Surd[3,4],10,120][[1]] (* Harvey P. Dale, Mar 09 2019 *)

PARI
```
2/3^(1/4)
```
PARI
```
2/sqrt(sqrt(3))
```

A154605 = 2/A011002 = 2/(3^(1/4)).

A179047 Decimal expansion of 9*sqrt(3)/4, the area of an equilateral triangle of side length 3.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 26 2010

			3.89711431702997391043675426838821282562131182107335641312556570376684...

Cf. A002194, A010502, A120011.

a=b=c=3;area=Sqrt[(a+b-c)*(a-b+c)*(-a+b+c)*(a+b+c)]/4;RealDigits[N[area,200]]
RealDigits[9 Sqrt[3]/4,10,120][[1]] (* Harvey P. Dale, Apr 27 2025 *)

A179050 Decimal expansion of 5/(2sqrt(5+2sqrt(5))), area of regular pentagram with base edge length 1.

Original entry on oeis.org

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

Offset: 0

Vladimir Joseph Stephan Orlovsky, Jun 26 2010

An algebraic number of degree 4: the smaller positive root of 16x^4 - 200x^2 + 125. - Charles R Greathouse IV, Dec 03 2012

			0.81229924058226581538967853053783616238725867880368775076951179784168...

Thomas M. Green, Area of Pentagram
Index entries for algebraic numbers, degree 4

Cf. A002194, A010502, A102771, A120011, A179047, A179048, A104956.

a=1;area=5/(2*Sqrt[5+2*Sqrt[5]]);RealDigits[N[area,20]]

5/sqrt(20+8*sqrt(5)) \\ Charles R Greathouse IV, Dec 03 2012

Offset corrected, keyword:cons inserted by R. J. Mathar, Jun 28 2010

Name corrected by Charles R Greathouse IV, Dec 03 2012

A308358 Beatty sequence for sqrt(3)/4.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 32, 33, 33, 34, 34

Offset: 0

R. J. Mathar, May 22 2019

Differs from A057357 first at n=37.

Index to sequences related to Beatty sequences

Cf. A120011.

Floor[Sqrt[3] Range[0, 100]/4] (* Wesley Ivan Hurt, Dec 26 2023 *)

a(n) = floor(n*A120011).

A171971(n) = a(n^2).

cp's OEIS Frontend

A178818 Decimal expansion of the diameter of the regular 7-gon (heptagon) of edge length 1.

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A385506 Decimal expansion of the volume of a triaugmented triangular prism with unit edge.

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A364895 Decimal expansion of the 4-volume of the unit regular pentachoron (5-cell).

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A343486 Decimal expansion of (29/96)*sqrt(3).

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A386001 Decimal expansion of the surface area of a tridiminished icosahedron with unit edge.

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A386003 Decimal expansion of the surface area of an augmented tridiminished icosahedron with unit edge.

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A154605 Decimal expansion of 2/(4th root of 3).

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A179050 Decimal expansion of 5/(2sqrt(5+2sqrt(5))), area of regular pentagram with base edge length 1.