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

Author

Clark Kimberling, Apr 10 2011

Keywords

• nonn
• cons

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,...

Examples

			1.3440306508910550179757754022548047678289849837719799753005...
		

Links

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

Crossrefs

Cf. A188640, A188658, A188659, A188730.

Programs

Magma

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

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]

PARI

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