cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A384625 Decimal expansion of the surface area of a pentagonal orthobicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 05 2025

Keywords

Comments

The pentagonal orthobicupola is Johnson solid J_30.
Also the surface area of a pentagonal gyrobicupola (Johnson solid J_31) with unit edge.

Examples

			17.771081820100127079336639808541900116171761474546...

Links

Crossrefs

Cf. A384624 (volume).
Cf. A002163, A384284, A384286, A384872.

Programs

  • Mathematica
    First[RealDigits[10 + Sqrt[5*(10 + Sqrt[5] + Sqrt[75 + 30*Sqrt[5]])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J30", "SurfaceArea"], 10, 100]]

Formula

Equals 10 + sqrt(5*(10 + sqrt(5) + sqrt(75 + 30*sqrt(5)))/2) = 10 + sqrt(5*(10 + A002163 + sqrt(75 + 30*A002163))/2).
Equals the largest root of x^8 - 80*x^7 + 2700*x^6 - 50000*x^5 + 552750*x^4 - 3710000*x^3 + 14628125*x^2 - 30562500*x + 25328125.

A384871 Decimal expansion of the volume of a pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 11 2025

Keywords

Comments

The pentagonal orthocupolarotunda is Johnson solid J_32.
Also the volume of a pentagonal gyrocupolarotunda (Johnson solid J_33) with unit edge.

Examples

			9.2418082864578952008524451431901588238346215825240...

Links

Crossrefs

Cf. A384872 (surface area).
Cf. A002163, A384144, A384283, A384285, A384624.

Programs

  • Mathematica
    First[RealDigits[5*(11 + 5*Sqrt[5])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5)) = (5/12)*(11 + 5*A002163).
Equals the largest root of 36*x^2 - 330*x - 25.

A384911 Decimal expansion of the surface area of an elongated pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 13 2025

Keywords

Comments

The elongated pentagonal orthocupolarotunda is Johnson solid J_40.
Also the surface area of an elongated pentagonal gyrocupolarotunda (Johnson solid J_41) with unit edge.

Examples

			33.538532332506058310041007622367288571887138891860...

Links

Crossrefs

Cf. A384910 (volume).
Cf. A002163, A384284, A384286, A384625.
Apart from the leading digit the same as A384872.

Programs

  • Mathematica
    First[RealDigits[(60 + Sqrt[10*(190 + 49*Sqrt[5] + 21*Sqrt[75 + 30*Sqrt[5]])])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J40", "SurfaceArea"], 10, 100]]

Formula

Equals (60 + sqrt(10*(190 + 49*sqrt(5) + 21*sqrt(75 + 30*sqrt(5)))))/4 = (60 + sqrt(10*(190 + 49*A002163 + 21*sqrt(75 + 30*A002163))))/4.
Equals the largest root of 256*x^8 - 30720*x^7 + 1491200*x^6 - 37440000*x^5 + 509444000*x^4 - 3437040000*x^3 + 5993612500*x^2 + 44939625000*x - 172099671875.
Showing 1-3 of 3 results.

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