A159550 Decimal expansion of (91443+58282*sqrt(2))/199^2.

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

Offset: 1

Author

Klaus Brockhaus, Apr 14 2009

Keywords

• cons
• nonn

Comments

lim_{n -> infinity} b(n)/b(n-1) = (91443+58282*sqrt(2))/199^2 for n mod 3 = 0, b = A129993.

lim_{n -> infinity} b(n)/b(n-1) = (91443+58282*sqrt(2))/199^2 for n mod 3 = 1, b = A159548.

Examples

			(91443+58282*sqrt(2))/199^2 = 4.39044960587431442726...
		

Links

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

Crossrefs

Cf. A129993, A159548, A002193 (decimal expansion of sqrt(2)), A159549 (decimal expansion of (201+20*sqrt(2))/199).

Programs

Magma

(91443 + 58282*Sqrt(2))/199^2; // G. C. Greubel, Mar 30 2018

Maple

with(MmaTranslator[Mma]): Digits:=100:
RealDigits(evalf((91443+58282*sqrt(2))/199^2))[1]; # Muniru A Asiru, Mar 31 2018

Mathematica

RealDigits[(91443+58282Sqrt[2])/199^2,10,120][[1]] (* Harvey P. Dale, Sep 23 2012 *)

PARI

(91443 + 58282*sqrt(2))/199^2 \\ G. C. Greubel, Mar 30 2018

Formula

(91443+58282*sqrt(2))/199^2 = (362+161*sqrt(2))/(362-161*sqrt(2))

= (3+2*sqrt(2))*(20-sqrt(2))^2/(20+sqrt(2))^2.