A159468 Decimal expansion of (34947+21922*sqrt(2))/127^2.

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

Offset: 1

Author

Klaus Brockhaus, Apr 13 2009

Keywords

• cons
• nonn
• easy

Comments

lim_{n -> infinity} b(n)/b(n-1) = (34947+21922*sqrt(2))/127^2 for n mod 3 = 0, b = A129992.

lim_{n -> infinity} b(n)/b(n-1) = (34947+21922*sqrt(2))/127^2 for n mod 3 = 1, b = A159466.

Examples

			(34947+21922*sqrt(2))/127^2 = 4.08887034002994541880...
		

Links

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

Crossrefs

Cf. A129992, A159466, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A159467 (decimal expansion of (129+16*sqrt(2))/127).

Programs

Magma

(34947 + 21922*Sqrt(2))/127^2; // G. C. Greubel, Mar 30 2018

Maple

with(MmaTranslator[Mma]): Digits:=100:
RealDigits(evalf((34947+21922*sqrt(2))/127^2))[1]; # Muniru A Asiru, Mar 31 2018

Mathematica

RealDigits[(34947+21922*Sqrt[2])/127^2,10,120][[1]] (* Harvey P. Dale, May 11 2012 *)

PARI

(34947+21922*sqrt(2))/127^2 \\ G. C. Greubel, Mar 30 2018

Formula

Equals (226+97*sqrt(2))/(226-97*sqrt(2)).

Equals (3+2*sqrt(2))*(16-sqrt(2))^2/(16+sqrt(2))^2.