A374359 -id:A374359 - cp's OEIS frontend

A374357 Decimal expansion of the 5th root of 109.

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

Offset: 1

Stefano Spezia, Jul 06 2024

			2.555555396735189817041820471280094045212814305...

Greg Martin and Winnie Miao, abc triples, arXiv:1409.2974 [math.NT], 2014. See p. 5.
Index entries for sequences related to the decimal expansion of the n-th root of x.

Cf. A374358 (continued fraction), A374359 (decimal expansion of the third convergent).

Mathematica
```
RealDigits[109^(1/5),10,100][[1]]
```

from sympy import integer_nthroot
def A374357(n): return integer_nthroot(109*10**(5*(n-1)),5)[0]%10 # Chai Wah Wu, Jul 07 2024

A378388 Decimal expansion of the surface area of a tetrakis hexahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Nov 27 2024

The tetrakis hexahedron is the dual polyhedron of the truncated octahedron.

			11.925695879998878380848926233233473255683297917928...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Tetrakis Hexahedron.

Cf. A374359 (volume - 1), A010532 (inradius*10), A179587 (midradius + 1), A378389 (dihedral angle).
Cf. A377341 (surface area of a truncated octahedron with unit edge).
Cf. A002163, A208899.

First[RealDigits[16*Sqrt[5]/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TetrakisHexahedron", "SurfaceArea"], 10, 100]]

Equals (16/3)*sqrt(5) = (16/3)*A002163 = 16*A208899.

A374358 Simple continued fraction of the 5th root of 109.

Original entry on oeis.org

2, 1, 1, 4, 77733, 2, 1, 1, 1, 3, 13, 1, 9715, 1, 3, 2, 1, 7, 1, 4, 52999, 1, 41, 2, 5, 1, 10019, 1, 1, 339, 5, 5, 52, 9, 20, 28, 2, 10, 2, 1, 27, 4, 1, 2, 8, 1, 1, 77, 1, 5, 9, 1, 10, 1, 5, 1, 1, 1, 4, 2, 4, 11, 1, 1, 1, 3, 2, 2, 4, 1, 15, 2, 26, 8, 1, 1, 1, 1, 46, 2

Offset: 0

Stefano Spezia, Jul 06 2024

			109^(1/5) = 2 + 1/(1 + 1/(1 + 1/(4 + 1/(77733 + ... )))).

Greg Martin and Winnie Miao, abc triples, arXiv:1409.2974 [math.NT], 2014. See p. 5.
Index entries for continued fractions for constants.

Cf. A374357 (decimal expansion), A374359 (decimal expansion of the third convergent).

Mathematica
```
ContinuedFraction[109^(1/5),80]
```

A378389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a tetrakis hexahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Nov 27 2024

The tetrakis hexahedron is the dual polyhedron of the truncated octahedron.

			2.498091544796508851659834154562180246155658808...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Tetrakis hexahedron.

Cf. A378388 (surface area), A374359 (volume - 1), A010532 (inradius*10), A179587 (midradius + 1).

Cf. A156546 and A195698 (dihedral angles of a truncated octahedron), A195729.

First[RealDigits[ArcCos[-4/5], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["TetrakisHexahedron", "DihedralAngles"]], 10, 100]]

Equals arccos(-4/5).

Equals 2*A195729. - Amiram Eldar, Nov 27 2024

A382004 Decimal expansion of the isoperimetric quotient of a tetrakis hexahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 17 2025

For the definition of isoperimetric quotient of a solid, references and links, see A381684.

			0.84297776772488716717876495718458737593598110244806...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

Cf. A378388 (surface area), A374359 (volume - 1).

Cf. A000796, A002163, A381684.

First[RealDigits[3*Pi/5/Sqrt[5], 10, 100]]

Equals 36*Pi*(A374359 + 1)^2/(A378388^3).

Equals 3*Pi/(5*sqrt(5)) = (3/5)*A000796/A002163.

cp's OEIS Frontend

A374357 Decimal expansion of the 5th root of 109.

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A378388 Decimal expansion of the surface area of a tetrakis hexahedron with unit shorter edge length.

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A374358 Simple continued fraction of the 5th root of 109.

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A378389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a tetrakis hexahedron.

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A382004 Decimal expansion of the isoperimetric quotient of a tetrakis hexahedron.

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