A160100 Decimal expansion of (361299 +5950*sqrt(2))/601^2.

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

Offset: 1

Author

Klaus Brockhaus, May 18 2009

Keywords

• cons
• nonn

Comments

lim_{n -> infinity} b(n)/b(n-1) = (361299+5950*sqrt(2))/601^2 for n mod 3 = 0, b = A111258.

lim_{n -> infinity} b(n)/b(n-1) = (361299+5950*sqrt(2))/601^2 for n mod 3 = 1, b = A160098.

Examples

			(361299+5950*sqrt(2))/601^2 = 1.02356740622567466740...
		

Links

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

Crossrefs

Cf. A111258, A160098, A002193 (decimal expansion of sqrt(2)), A160099 (decimal expansion of (843+418*sqrt(2))/601).

Programs

Magma

(361299+5950*Sqrt(2))/601^2; // G. C. Greubel, Apr 22 2018

Mathematica

RealDigits[(361299+5950*Sqrt[2])/601^2, 10, 100][[1]] (* G. C. Greubel, Apr 22 2018 *)

PARI

(361299+5950*sqrt(2))/601^2 \\ G. C. Greubel, Apr 22 2018

Formula

Equals (850 +7*sqrt(2))/(850 -7*sqrt(2)).

Equals (3 +2*sqrt(2))*(38 -11*sqrt(2))^2/(38 +11*sqrt(2))^2.