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A176458 Decimal expansion of 4+sqrt(17).

%I A176458 #21 Nov 15 2023 05:39:24
%S A176458 8,1,2,3,1,0,5,6,2,5,6,1,7,6,6,0,5,4,9,8,2,1,4,0,9,8,5,5,9,7,4,0,7,7,
%T A176458 0,2,5,1,4,7,1,9,9,2,2,5,3,7,3,6,2,0,4,3,4,3,9,8,6,3,3,5,7,3,0,9,4,9,
%U A176458 5,4,3,4,6,3,3,7,6,2,1,5,9,3,5,8,7,8,6,3,6,5,0,8,1,0,6,8,4,2,9,6,6,8,4,5,4
%N A176458 Decimal expansion of 4+sqrt(17).
%C A176458 Continued fraction expansion of 4+sqrt(17) is A010731.
%C A176458 This is the shape of an 8-extension rectangle; see A188640 for definitions.  - _Clark Kimberling_, Apr 09 2011
%H A176458 Wikipedia, <a href="https://en.wikipedia.org/wiki/Metallic_mean">Metallic mean</a>
%H A176458 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A176458 a(n) = A010473(n) for n > 1.
%F A176458 Equals exp(arcsinh(4)), since arcsinh(x)=log(x+sqrt(x^2+1)). - _Stanislav Sykora_, Nov 01 2013
%F A176458 Equals lim_{n->infinity} S(n, 2*sqrt(17))/S(n-1, 2*sqrt(17)), with the S-Chebyshev polynomials (see A049310). - _Wolfdieter Lang_, Nov 15 2023
%e A176458 4+sqrt(17) = 8.12310562561766054982...
%t A176458 r=8; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
%t A176458 N[t, 130]
%t A176458 RealDigits[N[t, 130]][[1]]
%o A176458 (PARI) 4+sqrt(17) \\ _Charles R Greathouse IV_, Jul 24 2013
%Y A176458 Cf. A010473 (decimal expansion of sqrt(17)), A010731 (all 8's sequence).
%Y A176458 Cf. A049310.
%K A176458 nonn,cons,easy
%O A176458 1,1
%A A176458 _Klaus Brockhaus_, Apr 20 2010