(MAGMAMagma) (8979+2990*Sqrt(2))/89^2; // G. C. Greubel, Apr 15 2018

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Equals lim_{n -> infinity} b(n)/b(n-1) = (8979+2990*sqrt(2))/89^2 for n mod 3 = 0, b = A129298.

Equals lim_{n -> infinity} b(n)/b(n-1) = (8979+2990*sqrt(2))/89^2 for n mod 3 = 1, b = A160055.

Equals (130+23*sqrt(2))/(130-23*sqrt(2)) = (3+2*sqrt(2))*(14- 3*sqrt(2) )^2/(14+3*sqrt(2))^2.

Equals (3+2*sqrt(2))*(14- 3*sqrt(2) )^2/(14+3*sqrt(2))^2.

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G. C. Greubel, <a href="/A160057/b160057.txt">Table of n, a(n) for n = 1..10000</a>

Equals (8979130+299023*sqrt(2))/89^2 = (130+-23*sqrt(2))/ = (3+2*sqrt(2))*(13014-23 3*sqrt(2) )^2/(14+3*sqrt(2))^2.

= (3+2*sqrt(2))*(14-3*sqrt(2))^2/(14+3*sqrt(2))^2.

RealDigits[(8979+2990*Sqrt[2])/89^2, 10, 100][[1]] (* G. C. Greubel, Apr 15 2018 *)

(PARI) (8979+2990*sqrt(2))/89^2 \\ G. C. Greubel, Apr 15 2018

(MAGMA) (8979+2990*Sqrt(2))/89^2; // G. C. Greubel, Apr 15 2018

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_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, May 04 2009

Decimal expansion of (8979+2990*sqrt(2))/89^2.

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

1,2

lim_{n -> infinity} b(n)/b(n-1) = (8979+2990*sqrt(2))/89^2 for n mod 3 = 0, b = A129298.

lim_{n -> infinity} b(n)/b(n-1) = (8979+2990*sqrt(2))/89^2 for n mod 3 = 1, b = A160055.

(8979+2990*sqrt(2))/89^2 = (130+23*sqrt(2))/(130-23*sqrt(2))

= (3+2*sqrt(2))*(14-3*sqrt(2))^2/(14+3*sqrt(2))^2.

(8979+2990*sqrt(2))/89^2 = 1.66740292279959022799...

Cf. A129298, A160055, A002193 (decimal expansion of sqrt(2)), A160056 (decimal expansion of (107+42*sqrt(2))/89).

cons,nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 04 2009

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