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 1-9 of 9 results.

A384284 Decimal expansion of the surface area of a gyroelongated pentagonal cupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 27 2025

Keywords

Comments

The gyroelongated pentagonal cupola is Johnson solid J_24.

Examples

			25.240003790832583513731278051892586452816662365...

Links

Crossrefs

Cf. A384283 (volume).
Cf. A002163, A002194, A179553, A179591, A179640, A384141.

Programs

  • Mathematica
    First[RealDigits[(20 + 25*Sqrt[3] + Sqrt[725 + 310*Sqrt[5]])/4, 10, 100]]
First[RealDigits[PolyhedronData["J24", "SurfaceArea"], 10, 100]]
  • PARI
    (20 + 25*sqrt(3) + sqrt(725 + 310*sqrt(5)))/4 \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals (20 + 25*sqrt(3) + sqrt(725 + 310*sqrt(5)))/4 = (20 + 25*A002194 + sqrt(725 + 310*A002163))/4.
Equals the largest root of 256*x^8 - 10240*x^7 + 12800*x^6 + 3200000*x^5 - 22476000*x^4 - 203280000*x^3 + 1412362500*x^2 + 3080375000*x - 17984046875.

A384285 Decimal expansion of the volume of a gyroelongated pentagonal rotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 29 2025

Keywords

Comments

The gyroelongated pentagonal rotunda is Johnson solid J_25.

Examples

			13.667050843671696932123530899233286565400264...

Links

Crossrefs

Cf. A384286 (surface area).
Cf. A002163, A179590, A179639, A179641, A384138, A384140, A384144, A384213, A384283.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*# + 10*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/12 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J25", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 10*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/12 = (45 + 17*A002163 + 10*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/12.
Equals the largest real root of 1679616*x^8 - 50388480*x^7 + 603262080*x^6 - 3520972800*x^5 + 5215460400*x^4 + 4128624000*x^3 - 8894943000*x^2 + 3881385000*x - 424924375.

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.

A385260 Decimal expansion of the volume of a gyroelongated pentagonal bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 27 2025

Keywords

Comments

The gyroelongated pentagonal bicupola is Johnson solid J_46.

Examples

			11.397378512213381124089433093505680212446879503678...

Links

Crossrefs

Cf. A385261 (surface area).
Cf. A002163, A384283, A385256, A385258.

Programs

  • Mathematica
    First[RealDigits[(10 + 8*# + 5*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/6 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J46", "Volume"], 10, 100]]

Formula

Equals (10 + 8*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (10 + 8*A002163 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.
Equals the largest real root of 6561*x^8 - 87480*x^7 + 313470*x^6 + 753300*x^5 - 22424850*x^4 - 84591000*x^3 - 85909500*x^2 + 8715000*x + 35547500.

A384909 Decimal expansion of the volume of an elongated pentagonal orthobicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 12 2025

Keywords

Comments

The elongated pentagonal orthobicupola is Johnson solid J_38.
Also the volume of an elongated pentagonal gyrobicupola (Johnson solid J_39) with unit edge.

Examples

			12.342299479604519768304624665067309540604246504993...

Links

Crossrefs

Cf. A384625 (surface area - 10).
Cf. A002163, A010476, A384283, A384624, A384871.

Programs

  • Mathematica
    First[RealDigits[(10 + 8*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J38", "Volume"], 10, 100]]

Formula

Equals (10 + 8*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (10 + 8*A002163 + 15*sqrt(5 + A010476))/6.
Equals the largest root of 1296*x^4 - 8640*x^3 - 82440*x^2 - 109200*x + 76525.

A384910 Decimal expansion of the volume of an elongated pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 13 2025

Keywords

Comments

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

Examples

			16.936017129396028707278171583282433383851376941...

Links

Crossrefs

Cf. A384911 (surface area).
Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909.

Programs

  • Mathematica
    First[RealDigits[5/12*(11 + 5*Sqrt[5] + 6*Sqrt[5 + Sqrt[20]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J40", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5) + 6*sqrt(5 + 2*sqrt(5))) = (5/12)*(11 + 5*A002163 + 6*sqrt(5 + A010476)).
Equals the largest root of 1296*x^4 - 23760*x^3 + 26100*x^2 + 84000*x - 111875.

A385262 Decimal expansion of the volume of a gyroelongated pentagonal cupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 27 2025

Keywords

Comments

The gyroelongated pentagonal cupolarotunda is Johnson solid J_47.

Examples

			15.991096162004890063062980011720804055694009940053...

Links

Crossrefs

Cf. A385263 (surface area).
Cf. A002163, A384283, A385256, A385258, A385260.

Programs

  • Mathematica
    First[RealDigits[5/12*(11 + 5*# + 2*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)]) & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J47", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5) + 2*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1))) = (5/12)*(11 + 5*A002163 + 2*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1))).
Equals the largest real root of 1679616*x^8 - 61585920*x^7 + 851472000*x^6 - 5108832000*x^5 + 4745790000*x^4 + 21346200000*x^3 - 29019375000*x^2 - 4576875000*x - 405859375.

A385264 Decimal expansion of the volume of a gyroelongated pentagonal birotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 30 2025

Keywords

Comments

The gyroelongated pentagonal birotunda is Johnson solid J_48.

Examples

			20.5848138117963990020365269299359278989411403764...

Links

Crossrefs

Cf. A385488 (surface area).
Cf. A002163, A384283, A385260, A385262.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*# + 5*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/6 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J48", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (45 + 17*A002163 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.
Equals the largest real root of 6561*x^8 - 393660*x^7 + 9316620*x^6 - 108207900*x^5 + 601832025*x^4 - 1417189500*x^3 + 965841750*x^2 + 597667500*x - 668786875.

A384952 Decimal expansion of the volume of an elongated pentagonal orthobirotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 20 2025

Keywords

Comments

The elongated pentagonal orthobirotunda is Johnson solid J_42.
Also the volume of an elongated pentagonal gyrobirotunda (Johnson solid J_43) with unit edge.

Examples

			21.52973477918753764625171850149755722709850737774...

Links

Crossrefs

Cf. A179451 (surface area - 10), A344149 (surface area + 20).
Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909, A384910.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J42", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (45 + 17*A002163 + 15*sqrt(5 + A010476))/6.
Equals the largest root of 1296*x^4 - 38880*x^3 + 252360*x^2 - 329400*x - 332975.
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