A088543 -id:A088543 - cp's OEIS frontend

A140239 Decimal expansion of 3*sqrt(15)/4.

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

Offset: 1

Rick L. Shepherd, May 14 2008

Area of the obtuse scalene triangle with sides of lengths 2, 3 and 4, the scalene triangle with least integer side lengths.

This is the area of the ninth-smallest triangle with integer side lengths, or the eighth-smallest triangle if two smaller triangles with the same area are counted only once (see A331251). - Hugo Pfoertner, Feb 12 2020

			2.90473750965556266388444904983679970812469127896869311994068032458511231895...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Index entries for algebraic numbers, degree 2

Cf. A140240, A140241, A140242, A140243, A140244, A140245, A140246, A140247, A140248, A140249, A088543, A010472, A331250, A331251.

RealDigits[(3Sqrt[15])/4,10,120][[1]] (* Harvey P. Dale, Apr 03 2013 *)

3*sqrt(15)/4 = 3*A010472/4.

A140246 Decimal expansion of sqrt(15)/6.

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, May 14 2008

Inradius of the obtuse scalene triangle with sides of lengths 2, 3 and 4, the scalene triangle with least integer side lengths. Per the Weisstein link, the inradius is the area divided by the semiperimeter.

			0.64549722436790281419654423329706660180548695088193180443126229435224718198...

Daniel Starodubtsev, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Inradius.
Index entries for algebraic numbers, degree 2

Cf. A140239, A140240, A140241, A140242, A140243, A140244, A140245, A140247, A140248, A140249, A088543, A010472.

Equals sqrt(A331257(8)/A331258(8)) (squared inradii of triangles with integer sides).

RealDigits[Sqrt[15]/6,10,120][[1]] (* Harvey P. Dale, Mar 31 2013 *)

PARI
```
sqrt(15)/6
```

sqrt(15)/6 = A010472/6 = 2*A140239/9.

A140248 Decimal expansion of 0.3 * sqrt(15).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, May 14 2008

Exradius opposite the side of length 2 of the obtuse scalene triangle with sides of lengths 2, 3 and 4, the scalene triangle with least integer side lengths. See formulas in the Weisstein link.

Multiplied by 10, this is sqrt(135). - Alonso del Arte, Jan 06 2013

			1.16189500386222506555377961993471988324987651158747724797627212983404492758...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Exradius.
Index entries for algebraic numbers, degree 2

Cf. A140239, A140240, A140241, A140242, A140243, A140244, A140245, A140246, A140247, A140249, A088543, A010472.

RealDigits[(3/10)Sqrt[15], 10, 105][[1]] (* Alonso del Arte, Jan 06 2013 *)

PARI
```
0.3*sqrt(15)
```

0.3*sqrt(15) = 0.3*A010472 = 0.4*A140239 = 0.6*A088543 = 0.2*A140249.

A140247 Decimal expansion of 8/sqrt(15).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, May 14 2008

Circumradius of the obtuse scalene triangle with sides of lengths 2, 3 and 4, the scalene triangle with least integer side lengths. See formulas in the Weisstein link.

			2.06559111797728900542894154655061312577755824282218177418003934192719098236...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Circumradius.
Index entries for algebraic numbers, degree 2

Cf. A140239, A140240, A140241, A140242, A140243, A140244, A140245, A140246, A140248, A140249, A088543, A010472.

Equals sqrt(A331227(10)/A331228(10)) = sqrt(A331227(11)/A331228(11)), A331254, A331255, A331256 (list of triangles with integer sides sorted by circumradius).

RealDigits[8/Sqrt[15],10,120][[1]] (* Harvey P. Dale, May 06 2012 *)

PARI
```
8/sqrt(15)
```

8/sqrt(15) = 8/A010472.

A140249 Decimal expansion of 3*sqrt(15)/2.

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, May 14 2008

Exradius opposite the side of length 4 of the obtuse scalene triangle with sides of lengths 2, 3 and 4, the scalene triangle with least integer side lengths. See formulas in the Weisstein link.

			5.80947501931112532776889809967359941624938255793738623988136064917022463790...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Exradius.
Index entries for algebraic numbers, degree 2

Cf. A140239, A140240, A140241, A140242, A140243, A140244, A140245, A140246, A140247, A140248, A088543, A010472.

First[RealDigits[3 Sqrt[15]/2,10,100]] (* Paolo Xausa, Oct 30 2023 *)

PARI
```
3*sqrt(15)/2
```

3*sqrt(15)/2 = 3*A010472/2 = 2*A140239 = 3*A088543 = 5*A140248.

A176058 Decimal expansion of (3+sqrt(15))/2.

Original entry on oeis.org

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

Offset: 1

Klaus Brockhaus, Apr 07 2010

Continued fraction expansion of (3+sqrt(15))/2 is A176059.

			(3+sqrt(15))/2 = 3.43649167310370844258...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A010472 (decimal expansion of sqrt(15)), A176059 (repeat 3, 2).

First[RealDigits[(3 + Sqrt[15])/2, 10, 100]] (* Paolo Xausa, Jun 18 2024 *)

Equals 1.5 + A088543. [R. J. Mathar, Apr 12 2010]

cp's OEIS Frontend

A140239 Decimal expansion of 3*sqrt(15)/4.

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A140246 Decimal expansion of sqrt(15)/6.

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A140248 Decimal expansion of 0.3 * sqrt(15).

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A140247 Decimal expansion of 8/sqrt(15).

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A140249 Decimal expansion of 3*sqrt(15)/2.

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A176058 Decimal expansion of (3+sqrt(15))/2.

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