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%I #35 Apr 10 2024 23:19:36
%S 6,1,6,2,2,7,7,6,6,0,1,6,8,3,7,9,3,3,1,9,9,8,8,9,3,5,4,4,4,3,2,7,1,8,
%T 5,3,3,7,1,9,5,5,5,1,3,9,3,2,5,2,1,6,8,2,6,8,5,7,5,0,4,8,5,2,7,9,2,5,
%U 9,4,4,3,8,6,3,9,2,3,8,2,2,1,3,4,4,2,4,8,1,0,8,3,7,9,3,0,0,2,9,5,1,8,7,3,4
%N Decimal expansion of 3+sqrt(10).
%C Continued fraction expansion of 3+sqrt(10) is A010722.
%C This is the shape of a 6-extension rectangle; see A188640 for definitions. - _Clark Kimberling_, Apr 09 2011
%C c^n = c*A005668(n) + A005668(n-1). - _Gary W. Adamson_, Apr 04 2024
%H Daniel Starodubtsev, <a href="/A176398/b176398.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Metallic_mean">Metallic mean</a>.
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F a(n) = A010467(n) for n >= 2.
%F Equals exp(arcsinh(3)), since arcsinh(x) = log(x+sqrt(x^2+1)). - _Stanislav Sykora_, Nov 01 2013
%F Equals lim_{n->oo} S(n, 2*sqrt(10))/ S(n-1, 2*sqrt(10)), with the S-Chebyshev polynomials (see A049310). - _Wolfdieter Lang_, Nov 15 2023
%e 6.16227766016837933199...
%p Digits:=100; evalf(3+sqrt(10)); # _Wesley Ivan Hurt_, Mar 07 2014
%t r=6; t=(r+(4+r^2)^(1/2))/2; RealDigits[N[t,130]][[1]] (* _Clark Kimberling_, Apr 09 2011 *)
%o (PARI) 3+sqrt(10) \\ _Charles R Greathouse IV_, Jul 24 2013
%Y Cf. A010467 (decimal expansion of sqrt(10)), A010722 (all 6's sequence).
%Y Cf. A049310.
%K cons,nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Apr 16 2010
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