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A277390 Decimal expansion of 5-2*sqrt(5)+sqrt(25-10*sqrt(5))-sqrt(5-2*sqrt(5)).

%I A277390 #10 Feb 16 2025 08:33:36
%S A277390 1,4,2,5,9,1,9,9,9,8,1,5,9,5,9,1,3,5,2,0,6,5,5,4,2,9,6,6,1,3,2,5,0,1,
%T A277390 1,0,4,2,7,7,1,8,8,2,4,5,4,1,9,1,1,5,5,9,0,2,4,7,1,6,2,7,7,7,5,1,6,5,
%U A277390 7,3,2,6,1,6,8,2,4,3,1,8,5,4,3,6,4,0,3
%N A277390 Decimal expansion of 5-2*sqrt(5)+sqrt(25-10*sqrt(5))-sqrt(5-2*sqrt(5)).
%C A277390 Largest radius of five circles tangent to a circle of radius 1.
%C A277390 A quartic integer with minimal polynomial x^4 - 20x^3 + 10x^2 + 20x + 5. - _Charles R Greathouse IV_, Oct 12 2016
%H A277390 Eric W. Weisstein: <a href="https://mathworld.wolfram.com/SteinerChain.html">Steiner chain.</a> From MathWorld. A Wolfram Web Resource.
%H A277390 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F A277390 tan(Pi/5)*(tan(Pi/5)+sqrt(1+tan(Pi/5)^2)).
%e A277390 1.42591999815959135206...
%t A277390 RealDigits[5-2*Sqrt[5]+Sqrt[25-10*Sqrt[5]]-Sqrt[5-2*Sqrt[5]],10,120][[1]] (* _Harvey P. Dale_, May 20 2021 *)
%o A277390 (PARI) s=sqrt(5); t=5-2*s; sqrt(25-10*s)+t-sqrt(t) \\ _Charles R Greathouse IV_, Oct 12 2016
%Y A277390 Cf. A176394 (three circles), A014176 (four circles).
%K A277390 nonn,cons
%O A277390 1,2
%A A277390 _Martin Renner_, Oct 12 2016