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A176537 Decimal expansion of 5 + sqrt(26).

%I A176537 #30 Feb 11 2025 15:16:31
%S A176537 1,0,0,9,9,0,1,9,5,1,3,5,9,2,7,8,4,8,3,0,0,2,8,2,2,4,1,0,9,0,2,2,7,8,
%T A176537 1,9,8,9,5,6,3,7,7,0,9,4,6,0,9,9,5,9,6,4,0,7,5,8,4,9,7,0,8,0,4,4,2,5,
%U A176537 9,3,3,6,3,2,0,6,2,2,2,4,1,9,5,5,8,8,3,4,8,8,5,1,0,9,3,9,3,2,0,0,8,3,6,1,1
%N A176537 Decimal expansion of 5 + sqrt(26).
%C A176537 Continued fraction expansion of 5 + sqrt(26) is A010692.
%C A176537 This is the shape of a 10-extension rectangle; see A188640 for definitions. - _Clark Kimberling_, Apr 09 2011
%H A176537 Daniel Starodubtsev, <a href="/A176537/b176537.txt">Table of n, a(n) for n = 2..10000</a>
%H A176537 Wikipedia, <a href="https://en.wikipedia.org/wiki/Metallic_mean">Metallic mean</a>
%H A176537 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A176537 a(n) = A010481(n-2) for n > 3.
%F A176537 Equals exp(arcsinh(5)), since arcsinh(x) = log(x + sqrt(x^2 + 1)). - _Stanislav Sykora_, Nov 01 2013
%F A176537 Equals limit_{n->infinity} S(n, 2*sqrt(2*13))/ S(n-1, 2*sqrt(2*13)), with the S-Chebyshev polynomilas (see A049310). - _Wolfdieter Lang_, Nov 15 2023
%e A176537 5+sqrt(26) = 10.09901951359278483002...
%t A176537 r=10; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
%t A176537 N[t, 130]
%t A176537 RealDigits[N[t, 130]][[1]]
%t A176537 RealDigits[5+Sqrt[26],10,120][[1]] (* _Harvey P. Dale_, Jun 24 2013 *)
%o A176537 (PARI) 5+sqrt(26) \\ _Michel Marcus_, Jul 23 2018
%Y A176537 Cf. A010481 (decimal expansion of sqrt(26)), A010692 (all 10's sequence).
%K A176537 cons,nonn,easy
%O A176537 2,4
%A A176537 _Klaus Brockhaus_, Apr 24 2010