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

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

1,2

Comments

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, ...

Links

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

Index entries for algebraic numbers, degree 2.

Formula

Minimal polynomial: 5*x^2 - 3*x - 5. - Amiram Eldar, Jun 01 2026

Example

1.3440306508910550179757754022548047678289849837719799753005...

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A188640, A188658, A188659, A188730.

Sequence in context: A240669 A213201 A245843 * A222509 A222488 A222500

Adjacent sequences: A188726 A188727 A188728 * A188730 A188731 A188732

Keyword

nonn,cons,changed

Author

Clark Kimberling, Apr 10 2011

Status

approved