A010472 -id:A010472 - cp's OEIS frontend

A248244 Egyptian fraction representation of sqrt(15) (A010472) using a greedy function.

3, 2, 3, 26, 842, 1210718, 3125731485713, 19754948045006045983659938, 1065761639370207788402744631308304462734917602085737, 324026619188969581072902747191745217929877633476958459802312813323913819842709323919885352524528244937458

Offset: 0

Robert G. Wilson v, Oct 04 2014

nonn

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.

Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 15]]

A010513 Decimal expansion of square root of 60.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 7 followed by {1, 2, 1, 14} repeated. - Harry J. Smith, Jun 07 2009

With a different offset, decimal expansion of 0.6. In a unimodal distribution, the mean and median differ by at most 0.6 standard deviations (and this is sharp), see Basu & DasGupta. - Charles R Greathouse IV, Oct 01 2024

			7.745966692414833770358530799564799221665843410583181653175147532226966....

Harry J. Smith, Table of n, a(n) for n = 1..20000
Sanjib Basu and Anirban DasGupta, The Mean, Median, and Mode of Unimodal Distributions: A Characterization, Theory of Probability & Its Applications 41:2 (1997), pp. 210-223; alternative link.
Index entries for algebraic numbers, degree 2.

Cf. A040052 (continued fraction).

Cf. A010472, A011053, A020772, A020817.

RealDigits[N[Sqrt[60],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 25 2011 *)

{ default(realprecision, 20080); x=sqrt(60); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010513.txt", n, " ", d)); } \\ Harry J. Smith, Jun 07 2009

Equals 10 * sqrt(3/5) = 10 * Sum_{k>=0} (-1)^k * binomial(2*k,k)/6^k. - Amiram Eldar, Aug 03 2020

Equals 2*A010472 = A011053^2 = 30*A020772 = 1/A020817. - Hugo Pfoertner, Oct 02 2024

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

Original entry on oeis.org

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.

A092294 Decimal expansion of 3 + sqrt(15).

Original entry on oeis.org

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

Offset: 1

Felix Tubiana, Feb 05 2004

Equals n +n/(n +n/(n +n/(n +....))) for n = 6. See also A090388. - Stanislav Sykora, Jan 23 2014

			6.87298334620741688...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for algebraic numbers, degree 2

Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A090550 (n=5), A092290 (n=7), A090654 (n=8), A090655 (n=9), A090656 (n=10). - Stanislav Sykora, Jan 23 2014

RealDigits[3+Sqrt[15],10,120][[1]] (* Harvey P. Dale, Aug 29 2012 *)

sqrt(15)+3 \\ Charles R Greathouse IV, Apr 25 2016

Equals A010472 plus 3. - R. J. Mathar, Sep 08 2008

Equals 1/A176016 + 6. - Hugo Pfoertner, Mar 19 2024

A088543 Decimal expansion of sqrt(15)/2.

Original entry on oeis.org

1, 9, 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

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Nov 16 2003

This is the ratio of the base of an isosceles triangle to its height when the other two sides are each equal to twice the base.

Exradius opposite the side of length 3 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. - Rick L. Shepherd, May 14 2008

			1.93649167310370844258963269989119980541646085264579541329378688305674154596...

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. A010527.

Cf. A140239, A140246, A140247, A140248, A140249, A010472.

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

sqrt(15)/2 = A010472/2 = A140249/3. - Rick L. Shepherd, May 14 2008

More terms from Rick L. Shepherd, May 14 2008

A176110 Decimal expansion of sqrt(255).

Original entry on oeis.org

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

Offset: 2

Klaus Brockhaus, Apr 10 2010

Continued fraction expansion of sqrt(255) is A040239.

			sqrt(255) = 15.96871942267131199907...

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

Cf. A010472 (decimal expansion of sqrt(15)), A010473 (decimal expansion of sqrt(17)), A040239.

RealDigits[Sqrt[255],10,120][[1]] (* Harvey P. Dale, Mar 22 2017 *)

cp's OEIS Frontend

A248244 Egyptian fraction representation of sqrt(15) (A010472) using a greedy function.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A010513 Decimal expansion of square root of 60.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A140246 Decimal expansion of sqrt(15)/6.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A140248 Decimal expansion of 0.3 * sqrt(15).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A140247 Decimal expansion of 8/sqrt(15).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A092294 Decimal expansion of 3 + sqrt(15).