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A157648 Decimal expansion of (1539+850*sqrt(2))/31^2.

%I A157648 #12 Jul 14 2025 10:03:39
%S A157648 2,8,5,2,3,2,2,0,8,9,5,0,7,9,4,0,4,6,9,8,0,3,7,8,2,9,5,0,6,5,3,7,3,9,
%T A157648 1,9,5,4,0,5,0,1,6,7,4,7,2,1,1,6,6,0,6,2,6,6,3,9,1,0,2,7,8,5,9,4,3,9,
%U A157648 3,6,1,1,5,1,8,5,0,0,6,2,2,5,8,3,0,2,0,7,4,9,6,5,4,3,6,9,9,6,2,2,0,8,6,1,2
%N A157648 Decimal expansion of (1539+850*sqrt(2))/31^2.
%C A157648 Limit_{n -> oo} b(n)/b(n-1) = (1539+850*sqrt(2))/31^2 for n mod 3 = 0, b = A118674.
%C A157648 Limit_{n -> oo} b(n)/b(n-1) = (1539+850*sqrt(2))/31^2 for n mod 3 = 1, b = A157646.
%H A157648 G. C. Greubel, <a href="/A157648/b157648.txt">Table of n, a(n) for n = 1..10000</a>
%F A157648 Equals (50+17*sqrt(2))/(50-17*sqrt(2)).
%F A157648 Equals (3+2*sqrt(2))*(8-sqrt(2))^2/(8+sqrt(2))^2.
%e A157648 2.85232208950794046980...
%p A157648 with(MmaTranslator[Mma]): Digits:=100:
%p A157648 RealDigits(evalf((1539+850*sqrt(2))/31^2))[1]; # _Muniru A Asiru_, Mar 31 2018
%t A157648 RealDigits[(1539+850*Sqrt[2])/31^2, 10, 100][[1]] (* _G. C. Greubel_, Mar 30 2018 *)
%o A157648 (PARI) (1539+850*sqrt(2))/31^2 \\ _G. C. Greubel_, Mar 30 2018
%o A157648 (Magma) (1539+850*Sqrt(2))/31^2; // _G. C. Greubel_, Mar 30 2018
%Y A157648 Cf. A118674, A157646, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A157647 (decimal expansion of (33+8*sqrt(2))/31).
%K A157648 cons,nonn,easy
%O A157648 1,1
%A A157648 _Klaus Brockhaus_, Mar 11 2009