%I #16 Jul 05 2022 11:08:32
%S 7,8,8,7,4,8,2,1,9,3,6,9,6,0,6,1,0,3,0,2,0,3,1,9,4,1,5,3,7,0,8,1,5,4,
%T 7,8,0,4,3,7,9,3,8,4,1,3,7,7,7,2,5,1,7,9,5,4,6,3,8,4,7,8,1,4,8,9,1,3,
%U 8,2,3,2,3,1,0,9,6,5,3,1,4,0,8,3,7,8,4,6,5,7,8,5,3,4,3,5,2,8,7,7,9
%N Decimal expansion of solution to n/x = x-n for n = 7.
%C n/x = x-n with n=1 gives the Golden Ratio = 1.6180339887...
%C Equals n +n/(n +n/(n +n/(n +....))) for n = 7. See also A090388. - _Stanislav Sykora_, Jan 23 2014
%H Chai Wah Wu, <a href="/A092290/b092290.txt">Table of n, a(n) for n = 1..10001</a>
%F n/x = x-n ==> x^2 - n*x - n = 0 ==> x = (n + sqrt(n^2 + 4*n)) / 2 (Positive Root) n = 7: x = (7 + sqrt(77))/2 = 7.88748219369606...
%t RealDigits[(7+Sqrt[77])/2, 10, 50][[1]] (* _G. C. Greubel_, Jul 03 2017 *)
%o (PARI) (7+sqrt(77))/2 \\ _Charles R Greathouse IV_, Oct 18 2012
%Y Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A090550 (n=5), A092294 (n=6), A090654 (n=8), A090655 (n=9), A090656 (n=10). - _Stanislav Sykora_, Jan 23 2014
%K easy,nonn,cons
%O 1,1
%A _Felix Tubiana_, Feb 05 2004