A188733 Decimal expansion of (9+sqrt(145))/8.

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

Offset

1,1

Comments

Decimal expansion of shape of a (9/4)-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 (periodic) continued fraction of the constant is [2,1,1,1,2,2,1,1,1,2,2,1,...].

Links

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

Index entries for algebraic numbers, degree 2.

Formula

Minimal polynomial: 4*x^2 - 9*x - 4. - Amiram Eldar, Jun 06 2026

Example

2.6301993223490369350160301287973260065531690506317...

Maple

evalf((9+sqrt(145))/8, 120); # Muniru A Asiru, Nov 01 2018

Mathematica

r = 9/4; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
(* Alternative: *)
RealDigits[(9+Sqrt[145])/8, 10, 120][[1]] (* Harvey P. Dale, Jul 20 2025 *)

Prog

(PARI) (9+sqrt(145))/8 \\ Michel Marcus, Sep 03 2014
(Magma) SetDefaultRealField(RealField(100)); (9+Sqrt(145))/8; // G. C. Greubel, Nov 01 2018

Crossrefs

Cf. A188640.

Sequence in context: A271503 A102068 A351709 * A104290 A152549 A136759

Adjacent sequences: A188730 A188731 A188732 * A188734 A188735 A188736

Keyword

nonn,cons,changed

Author

Clark Kimberling, Apr 10 2011

Status

approved