A157472 Decimal expansion of (627 + 238*sqrt(2))/23^2.

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

Offset: 1

Author

Klaus Brockhaus, Mar 12 2009

Keywords

• cons
• nonn

Examples

			(627 + 238*sqrt(2))/23^2 = 1.82151763297693123178...
		

Links

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

Crossrefs

Cf. A118337, A156567, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A156571 (decimal expansion of (27+10*sqrt(2))/23).

Programs

Magma

SetDefaultRealField(RealField(100)); (627+238*sqrt(2))/23^2; // G. C. Greubel, Aug 17 2018

Mathematica

RealDigits[(627+238Sqrt[2])/23^2,10,120][[1]] (* Harvey P. Dale, Feb 03 2015 *)

PARI

(627 + 238*sqrt(2))/23^2 \\ G. C. Greubel, Aug 17 2018

Formula

Equals (34 + 7*sqrt(2))/(34 - 7*sqrt(2)) = (3+2*sqrt(2))*(10- 2*sqrt(2) )^2/(10+2*sqrt(2))^2.

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, where b is A118337.

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, where b is A156567.