A159692 Decimal expansion of (2052963 + 1343918*sqrt(2))/881^2.

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

Offset: 1

Author

Klaus Brockhaus, Apr 21 2009

Keywords

• cons
• nonn

Comments

Lim_{n -> infinity} b(n)/b(n-1) = (2052963+1343918*sqrt(2))/881^2 for n mod 3 = 0, b = A130014.

Lim_{n -> infinity} b(n)/b(n-1) = (2052963+1343918*sqrt(2))/881^2 for n mod 3 = 1, b = A159690.

Examples

			(2052963 + 1343918*sqrt(2))/881^2 = 5.09372419165266633056...
		

Links

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

Crossrefs

Cf. A130014, A159690, A002193 (decimal expansion of sqrt(2)), A159691 (decimal expansion of (883+42*sqrt(2))/881).

Programs

Magma

(2052963 + 1343918*Sqrt(2))/881^2; // G. C. Greubel, Jun 02 2018

Mathematica

RealDigits[(2052963 + 1343918*Sqrt[2])/881^2, 10, 100][[1]] (* G. C. Greubel, Jun 02 2018 *)

PARI

(2052963 + 1343918*sqrt(2))/881^2 \\ G. C. Greubel, Jun 02 2018

Formula

Equals (1682 + 799*sqrt(2))/(1682 - 799*sqrt(2)).

Equals (3 + 2*sqrt(2))*(42 - sqrt(2))^2/(42 + sqrt(2))^2.