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.

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A374883 Decimal expansion of phi*(2*phi + 1) (i.e., (7 + 3*sqrt(5))/2), where phi is the golden ratio.

Original entry on oeis.org

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

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Author

Marco Ripà, Jul 22 2024

Keywords

Comments

The author conjectures that this is the minimum volume of an axis-aligned bounding box which includes the shortest minimum-link circuit joining all the vertices of the cube {0,1}^3 (i.e., the closed polygonal chains consisting of exactly 6 edges visiting all the points of the set {(0,0,0),(0,0,1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0),(1,1,1)}).
In detail, such a circuit of 6 links is given by (1/2,1+phi,1/2)-((1-phi)/2,0,(1+phi)/2)-((phi+1)/2,0, (1-phi)/2)-(1/2,1+phi,1/2)-((phi+1)/2,0,(phi+1)/2)-((1-phi)/2,0,(1-phi)/2(1/2,1+phi,1/2), where phi := (1+sqrt(5))/2 (see A001622).
Then, phi*(2*phi + 1) = phi^2*(phi + 1) since phi - 1 = 1/phi.

Examples

			6.8541019662496845446137605030969...

References

  • Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, pages 138-139.

Links

Crossrefs

Cf. A001622, A090550, A104457, A134973, A205769, A225227, A261547, A363755, A373537, A374149, A374260.

Programs

  • Mathematica
    RealDigits[3*GoldenRatio + 2, 10, 120][[1]] (* Amiram Eldar, Jul 23 2024 *)

Formula

Equals (7 + 3*sqrt(5))/2.
Equals phi^2*(phi + 1), where phi = (1 + sqrt(5))/2.
Equals A104457^2 = 2*A205769. - Hugo Pfoertner, Jul 22 2024
Equals A090550 + 1 = A134973 + 5. - Amiram Eldar, Jul 23 2024
Equals phi^4. - Stefano Spezia, May 28 2025

A374948 Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.

Original entry on oeis.org

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

Views

Author

Marco Ripà, Jul 24 2024

Keywords

Comments

The 1994 Bridge's paper entitled "Minimal Steiner Trees for Three Dimensional Networks" (see Links) suggested an optimal strategy to solve the minimum Steiner tree problem for the unit cube {0,1}^3, and the total length of the provided Steiner Tree is 1 + 3*sqrt(3).
Also the surface area of a gyroelongated square pyramid (Johnson solid J_10) with unit edges. - Paolo Xausa, Aug 04 2025

Examples

			6.1961524227066318805823390245176171008284157614311418841674209383...

Links

Crossrefs

Cf. A002194, A010482, A374148, A374260.
Essentially the same as A178809, A176532 and A010482.

Programs

  • Mathematica
    RealDigits[3Sqrt[3]+1,10,87][[1]] (* Stefano Spezia, Jul 25 2024 *)

Formula

Equals 3*sqrt(3) + 1.
Equals A010482(n) for any n >= 2 and a(1) = A010482(1) + 1.
Showing 1-2 of 2 results.

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