A160214 Decimal expansion of (1947891+1218490*sqrt(2))/953^2.

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

Offset: 1

Author

Klaus Brockhaus, May 18 2009

Keywords

• cons
• nonn

Comments

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129975.

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160212.

Examples

			(1947891+1218490*sqrt(2))/953^2 = 4.04212695934084840165...
		

Links

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

Crossrefs

Cf. A129975, A160212, A002193 (decimal expansion of sqrt(2)), A160213 (decimal expansion of (969+124*sqrt(2))/953).

Programs

Magma

(1947891 +1218490*Sqrt(2))/953^2; // G. C. Greubel, Apr 08 2018

Mathematica

RealDigits[(1947891 +1218490*Sqrt[2])/953^2, 10, 100][[1]] (* G. C. Greubel, Apr 08 2018 *)

PARI

(1947891 +1218490*sqrt(2))/953^2 \\ G. C. Greubel, Apr 08 2018

Formula

Equals (1690+721*sqrt(2))/(1690-721*sqrt(2)).

Equals (3+2*sqrt(2))*(31-2*sqrt(2))^2/(31+2*sqrt(2))^2.