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A090655 Decimal expansion of solution to n/x = x-n for n = 9. 9

%I

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

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

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

%N Decimal expansion of solution to n/x = x-n for n = 9.

%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 = 9. See also A090388. - _Stanislav Sykora_, Jan 23 2014

%H G. C. Greubel, <a href="/A090655/b090655.txt">Table of n, a(n) for n = 1..10000</a>

%F n/x = x-n ==> x^2 - n*x - n = 0 ==> x = (n + sqrt(n^2 + 4*n)) / 2 (Positive Root) n = 9: x = (9 + sqrt(117))/2 = 9.90832691319598...

%F Equals (3/2)*(3 + sqrt(13)). - _G. C. Greubel_, Jul 03 2017

%e 9.90832691319598...

%t RealDigits[(3/2)*(3+Sqrt[13]), 10, 50][[1]] (* _G. C. Greubel_, Jul 03 2017 *)

%o (PARI) (3/2)*(3 + sqrt(13)) \\ _G. C. Greubel_, Jul 03 2017

%Y Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A090550 (n=5), A092294 (n=6), A092290 (n=7), A090654 (n=8), A090656 (n=10). - _Stanislav Sykora_, Jan 23 2014

%K easy,nonn,cons

%O 1,1

%A Felix Tubiana (fat2(AT)columbia.edu), Feb 05 2004

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Last modified July 5 20:21 EDT 2020. Contains 335473 sequences. (Running on oeis4.)