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A157472 Decimal expansion of (627 + 238*sqrt(2))/23^2.

%I A157472 #10 Sep 08 2022 08:45:42
%S A157472 1,8,2,1,5,1,7,6,3,2,9,7,6,9,3,1,2,3,1,7,8,6,0,1,4,9,6,4,7,6,7,3,1,2,
%T A157472 1,7,9,0,1,6,2,2,2,8,8,5,3,3,0,2,7,1,5,3,3,8,6,7,7,6,8,9,5,5,8,4,4,6,
%U A157472 0,1,7,5,7,7,9,5,8,0,6,1,9,1,3,9,2,0,4,5,8,0,9,3,9,5,0,4,4,7,9,0,7,5,7,9,0
%N A157472 Decimal expansion of (627 + 238*sqrt(2))/23^2.
%H A157472 G. C. Greubel, <a href="/A157472/b157472.txt">Table of n, a(n) for n = 1..10000</a>
%F A157472 Equals (34 + 7*sqrt(2))/(34 - 7*sqrt(2)) = (3+2*sqrt(2))*(10- 2*sqrt(2) )^2/(10+2*sqrt(2))^2.
%F A157472 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, where b is A118337.
%F A157472 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, where b is A156567.
%e A157472 (627 + 238*sqrt(2))/23^2 = 1.82151763297693123178...
%t A157472 RealDigits[(627+238Sqrt[2])/23^2,10,120][[1]] (* _Harvey P. Dale_, Feb 03 2015 *)
%o A157472 (PARI) (627 + 238*sqrt(2))/23^2 \\ _G. C. Greubel_, Aug 17 2018
%o A157472 (Magma) SetDefaultRealField(RealField(100)); (627+238*sqrt(2))/23^2; // _G. C. Greubel_, Aug 17 2018
%Y A157472 Cf. A118337, A156567, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A156571 (decimal expansion of (27+10*sqrt(2))/23).
%K A157472 cons,nonn
%O A157472 1,2
%A A157472 _Klaus Brockhaus_, Mar 12 2009