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A157300 Decimal expansion of (1683 + 58*sqrt(2))/41^2.

%I A157300 #16 Oct 05 2024 18:15:54
%S A157300 1,0,4,9,9,8,4,7,6,3,0,0,8,7,0,8,8,1,1,9,1,5,8,2,2,6,9,2,4,4,7,4,4,9,
%T A157300 4,2,8,0,5,2,9,6,9,0,4,7,4,5,5,0,0,4,7,5,2,0,7,8,6,7,1,8,7,6,7,4,2,0,
%U A157300 9,5,4,6,9,2,1,5,2,3,0,3,4,3,9,9,3,6,4,8,1,1,2,4,2,7,7,2,3,5,0,4,5,9,1,6,8
%N A157300 Decimal expansion of (1683 + 58*sqrt(2))/41^2.
%C A157300 Limit_{n -> oo} b(n)/b(n-1) = (1683+58*sqrt(2))/41^2 for n mod 3 = 0, b = A129288.
%C A157300 Limit_{n -> oo} b(n)/b(n-1) = (1683+58*sqrt(2))/41^2 for n mod 3 = 1, b = A157257.
%H A157300 G. C. Greubel, <a href="/A157300/b157300.txt">Table of n, a(n) for n = 1..10000</a>
%F A157300 Equals (58+sqrt(2))/(58-sqrt(2)).
%F A157300 Equals (3+2*sqrt(2))*(7-2*sqrt(2))^2/(7+2*sqrt(2))^2.
%e A157300 (1683+58*sqrt(2))/41^2 = 1.04998476300870881191...
%p A157300 evalf((1683+58*sqrt(2))/41^2,120); # _Muniru A Asiru_, Sep 28 2018
%t A157300 RealDigits[(1683+58Sqrt[2])/41^2,10,120][[1]] (* _Harvey P. Dale_, May 05 2014 *)
%o A157300 (PARI) default(realprecision, 100); (1683+58*sqrt(2))/41^2 \\ _G. C. Greubel_, Sep 28 2018
%o A157300 (Magma) SetDefaultRealField(RealField(100)); (1683+58*Sqrt(2))/41^2; // _G. C. Greubel_, Sep 28 2018
%Y A157300 Cf. A129288, A157257, A002193 (decimal expansion of sqrt(2)), A157260 (decimal expansion of (57+28*sqrt(2))/41).
%K A157300 cons,nonn
%O A157300 1,3
%A A157300 _Klaus Brockhaus_, May 01 2009