A157648 - OEIS

%I #8 Sep 08 2022 08:45:42

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

%C lim_{n -> infinity} b(n)/b(n-1) = (1539+850*sqrt(2))/31^2 for n mod 3 = 0, b = A118674.

%C lim_{n -> infinity} b(n)/b(n-1) = (1539+850*sqrt(2))/31^2 for n mod 3 = 1, b = A157646.

%H G. C. Greubel, <a href="/A157648/b157648.txt">Table of n, a(n) for n = 1..10000</a>

%F (1539+850*sqrt(2))/31^2 = (50+17*sqrt(2))/(50-17*sqrt(2))

%F = (3+2*sqrt(2))*(8-sqrt(2))^2/(8+sqrt(2))^2.

%e (1539+850*sqrt(2))/31^2 = 2.85232208950794046980...

%p with(MmaTranslator[Mma]): Digits:=100:

%p RealDigits(evalf((1539+850*sqrt(2))/31^2))[1]; # _Muniru A Asiru_, Mar 31 2018

%t Realdigits[(1539+850*Sqrt[2])/31^2, 10, 100][[1]] (* _G. C. Greubel_, mar 30 2018 *)

%o (PARI) (1539+850*sqrt(2))/31^2 \\ _G. C. Greubel_, Mar 30 2018

%o (Magma) (1539+850*Sqrt(2))/31^2; // _G. C. Greubel_, Mar 30 2018

%Y 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 cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Mar 11 2009