A188730 -id:A188730 - cp's OEIS frontend

A188659 Decimal expansion of (1+sqrt(26))/5.

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

Offset: 1

Clark Kimberling, Apr 09 2011

Decimal expansion of the shape of a (2/5)-extension rectangle; see A188640 for definitions of shape and r-extension rectangle. Briefly, shape=length/width, and an r-extension rectangle is composed of two rectangles of shape 1/r when r<1.

The continued fraction of the constant is 1, 4, 1, 1, 4, 1, ... = A146325.

			1.219803902718556966005644821804556397912754189219919281516994...

Index entries for algebraic numbers, degree 2.

Cf. A146325, A188640, A188658, A188729, A188730, A010481.

RealDigits[(1 + Sqrt[26])/5, 10, 111][[1]] (* Robert G. Wilson v, Aug 18 2011 *)

Equals exp(arcsinh(1/5)). - Amiram Eldar, Jul 04 2023

A344382 Decimal expansion of sqrt(29)/5.

Original entry on oeis.org

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

Offset: 1

Wesley Ivan Hurt, May 18 2021

Essentially the same as A188730 after the first two initial terms.

sqrt(29)/5 is the length of the shortest line segment needed to dissect the unit square into 5 regions with equal areas if all the line segments start at the same vertex of the square.

			1.07703296142690080625014209...

Cf. A344069, A188730.

Mathematica
```
RealDigits[Sqrt[29]/5, 10, 200][[1]]
```

A188729 Decimal expansion of (3+sqrt(109))/10.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Apr 10 2011

Decimal expansion of shape of a (3/5)-extension rectangle; see A188640 for definitions of shape and r-extension rectangle.
Briefly, shape=length/width, and an r-extension rectangle is composed of two rectangles of shape 1/r when r<1.
The continued fraction of the constant is 1, 2, 1, 9, 1, 2, 1, 1, 2, 1, 9, 1, 2, 1, 1, 2, 1, 9, 1, 2, 1,...

			1.3440306508910550179757754022548047678289849837719799753005...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A188640, A188658, A188659, A188730.

SetDefaultRealField(RealField(100)); (3+Sqrt(109))/10; // G. C. Greubel, Nov 01 2018

evalf((3+sqrt(109))/10,140); # Muniru A Asiru, Nov 01 2018

r = 3/5; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]

default(realprecision, 100); (3+sqrt(109))/10 \\ G. C. Greubel, Nov 01 2018

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A188659 Decimal expansion of (1+sqrt(26))/5.

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A344382 Decimal expansion of sqrt(29)/5.

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A188729 Decimal expansion of (3+sqrt(109))/10.

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