A190181 Decimal expansion of (15+sqrt(465))/12.

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

Offset

1,1

Comments

The rectangle R whose shape (i.e., length/width) is (15+sqrt(465))/12 can be partitioned into rectangles of shapes 5/2 and 3/2 in a manner that matches the periodic continued fraction [5/2, 3/2, 5/2, 3/2,...]. R can also be partitioned into squares so as to match the periodic continued fraction [3,21,3,1,1,4,1,4,1,1,3,21,...]. For details, see A188635.

Links

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

Example

3.046988221070652056227828483250098729807...

Mathematica

FromContinuedFraction[{5/2, 3/2, {5/2, 3/2}}]
FullSimplify[%]
ContinuedFraction[%, 100]  (* [3, 21, 3, 1, 1, 4, 1, 4, 1, 1, 3, 21, ...] *)
RealDigits[N[%%, 120]]      (* A190181 *)
N[%%%, 40]
RealDigits[(15+Sqrt[465])/12, 10, 100][[1]] (* G. C. Greubel, Dec 28 2017 *)

Prog

(PARI) (15+sqrt(465))/12 \\ G. C. Greubel, Dec 28 2017
(Magma) [(15+sqrt(465))/12]; // G. C. Greubel, Dec 28 2017

Crossrefs

Cf. A188635.

Sequence in context: A197022 A112238 A111493 * A145092 A210878 A355977

Adjacent sequences: A190178 A190179 A190180 * A190182 A190183 A190184

Keyword

nonn,cons

Author

Clark Kimberling, May 05 2011

Status

approved