A159759 - OEIS

%I #14 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (83+18*sqrt(2))/79.

%C Equals Lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A118676.

%C Equals Lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A159758.

%H G. C. Greubel, <a href="/A159759/b159759.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (9 + sqrt(2))/(9 - sqrt(2)).

%e (83+18*sqrt(2))/79 = 1.37285878636349001111...

%t RealDigits[(83+18Sqrt[2])/79,10,120][[1]] (* _Harvey P. Dale_, Jul 27 2017 *)

%o (PARI) (18*sqrt(2)+83)/79 \\ _Charles R Greathouse IV_, Jan 30 2018

%o (Magma) (83 +18*Sqrt(2))/79; // _G. C. Greubel_, May 22 2018

%Y Cf. A118676, A159758, A002193 (decimal expansion of sqrt(2)), A159760 (decimal expansion of (10659+6110*sqrt(2))/79^2).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, Apr 30 2009