A188731 Decimal expansion of (5+sqrt(41))/4.

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

Offset: 1

Author

Clark Kimberling, Apr 10 2011

Keywords

• nonn
• cons

Comments

Decimal expansion of shape of a (5/2)-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 r.

The continued fractions of the constant are 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1...

Examples

			2.850781059358212171622054418655453316130105033155254721...
		

Links

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

Crossrefs

Cf. A188640.

Programs

Magma

SetDefaultRealField(RealField(100)); (5+Sqrt(41))/4; // G. C. Greubel, Nov 01 2018

Maple

evalf((5+sqrt(41))/4,140); # Muniru A Asiru, Nov 01 2018

Mathematica

r = 5/2; 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); (5+sqrt(41))/4 \\ G. C. Greubel, Nov 01 2018