A159895 - OEIS

%I #6 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (1304787+843542*sqrt(2))/727^2.

%C lim_{n -> infinity} b(n)/b(n-1) = (1304787+843542*sqrt(2))/727^2 for n mod 3 = 0, b = A130646.

%C lim_{n -> infinity} b(n)/b(n-1) = (1304787+843542*sqrt(2))/727^2 for n mod 3 = 1, b = A159893.

%H G. C. Greubel, <a href="/A159895/b159895.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (1354 +623*sqrt(2))/(1354 -623*sqrt(2)).

%F Equals (3 +2*sqrt(2))*(27 -sqrt(2))^2/(27 +sqrt(2))^2.

%e (1304787+843542*sqrt(2))/727^2 = 4.72582495346769116482...

%t RealDigits[(1304787+843542*Sqrt[2])/727^2, 10, 100][[1]] (* _G. C. Greubel_, May 17 2018 *)

%o (PARI) (1304787 +843542*sqrt(2))/727^2 \\ _G. C. Greubel_, May 17 2018

%o (Magma) (1304787 +843542*Sqrt(2))/727^2; // _G. C. Greubel_, May 17 2018

%Y Cf. A130646, A159893, A002193 (decimal expansion of sqrt(2)), A159894 (decimal expansion of (731+54*sqrt(2))/727).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 30 2009