A160177 - OEIS

%I #10 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (633+100*sqrt(2))/617.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A115135.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160176.

%H G. C. Greubel, <a href="/A160177/b160177.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (25 +2*sqrt(2))/(25 -2*sqrt(2)).

%e (633+100*sqrt(2))/617 = 1.25513996148672529153...

%t RealDigits[(633+100Sqrt[2])/617,10,120][[1]] (* _Harvey P. Dale_, Nov 25 2013 *)

%o (PARI) (633+100*sqrt(2))/617 \\ _G. C. Greubel_, Apr 25 2018

%o (Magma) (633+100*Sqrt(2))/617; // _G. C. Greubel_, Apr 25 2018

%Y Cf. A115135, A160176, A002193 (decimal expansion of sqrt(2)), A160178 (decimal expansion of (755667+461578*sqrt(2))/617^2).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, May 18 2009