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Decimal expansion of (52323 + 26522*sqrt(2))/191^2.
4

%I #14 Sep 08 2022 08:45:45

%S 2,4,6,2,3,9,8,8,4,0,5,2,6,8,2,8,4,0,0,6,5,5,6,3,9,6,0,2,6,2,8,4,8,0,

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

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

%N Decimal expansion of (52323 + 26522*sqrt(2))/191^2.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A161486.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A161487.

%H G. C. Greubel, <a href="/A161489/b161489.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (298 + 89*sqrt(2))/(298 - 89*sqrt(2)).

%F Equals (3 + 2*sqrt(2))*(20 - 3*sqrt(2))^2/(20 + 3*sqrt(2))^2.

%e (52323 + 26522*sqrt(2))/191^2 = 2.46239884052682840065...

%t RealDigits[(52323+26522*Sqrt[2])/191^2, 10, 100][[1]] (* _G. C. Greubel_, Apr 06 2018 *)

%o (PARI) (52323 + 26522*sqrt(2))/191^2 \\ _G. C. Greubel_, Apr 06 2018

%o (Magma) (52323 + 26522*Sqrt(2))/191^2; // _G. C. Greubel_, Apr 06 2018

%Y Cf. A161486, A161487, A002193 (decimal expansion of sqrt(2)), A161488 (decimal expansion of (209+60*sqrt(2))/191).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Jun 13 2009