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

1,1

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...

Links

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

Example

2.850781059358212171622054418655453316130105033155254721...

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]

Prog

(PARI) default(realprecision, 100); (5+sqrt(41))/4 \\ G. C. Greubel, Nov 01 2018
(Magma) SetDefaultRealField(RealField(100)); (5+Sqrt(41))/4; // G. C. Greubel, Nov 01 2018

Crossrefs

Cf. A188640.

Sequence in context: A011058 A368644 A229981 * A188617 A154157 A197150

Adjacent sequences: A188728 A188729 A188730 * A188732 A188733 A188734

Keyword

nonn,cons

Author

Clark Kimberling, Apr 10 2011

Status

approved