A157299 Decimal expansion of (82611+44030*sqrt(2))/233^2.

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

Offset: 1

Author

Klaus Brockhaus, Apr 11 2009

Keywords

• cons
• nonn

Comments

lim_{n -> infinity} b(n)/b(n-1) = (82611+44030*sqrt(2))/233^2 for n mod 3 = 0, b = A129625.

lim_{n -> infinity} b(n)/b(n-1) = (82611+44030*sqrt(2))/233^2 for n mod 3 = 1, b = A157297.

Examples

			(82611+44030*sqrt(2))/233^2 = 2.66865890237962340434...
		

Links

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

Crossrefs

Cf. A129625, A157297, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A157298 (decimal expansion of (251+66*sqrt(2))/233).

Programs

Magma

(82611+44030*Sqrt(2))/233^2; // G. C. Greubel, Mar 29 2018

Mathematica

RealDigits[(82611+44030Sqrt[2])/233^2,10,120][[1]] (* Harvey P. Dale, Feb 25 2014 *)

PARI

(82611+44030*sqrt(2))/233^2 \\ G. C. Greubel, Mar 29 2018

Formula

(82611+44030*sqrt(2))/233^2 = (370+119*sqrt(2))/(370-119*sqrt(2))

= (3+2*sqrt(2))*(22-3*sqrt(2))^2/(22+3*sqrt(2))^2.