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A222134 Decimal expansion of sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + ... )))).

%I A222134 #22 Jul 02 2025 10:58:52
%S A222134 2,7,9,1,2,8,7,8,4,7,4,7,7,9,2,0,0,0,3,2,9,4,0,2,3,5,9,6,8,6,4,0,0,4,
%T A222134 2,4,4,4,9,2,2,2,8,2,8,8,3,8,3,9,8,5,9,5,1,3,0,3,6,2,1,0,6,1,9,5,3,4,
%U A222134 3,4,2,1,2,7,7,3,8,8,5,4,4,3,3,0,2,1,8,0,7,7,9,7,4,6,7,2,2,5,1,6,3
%N A222134 Decimal expansion of sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + ... )))).
%C A222134 c^n = A015440(n) + A015440(n-1) * A222135, where c = (1 + sqrt(21))/2 and A222135 = (-1 + sqrt(21))/2. - _Gary W. Adamson_, Nov 27 2023
%H A222134 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A222134 Equals (sqrt(21) + 1)/2 = A090458 - 1 = A107905 - 2 = A222135 + 1.
%F A222134 sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + ... )))) - 1 = sqrt(5 - sqrt(5 - sqrt(5 - sqrt(5 - ... )))) = A222135.
%F A222134 Minimal polynomial: x^2 - x - 5. - _Stefano Spezia_, Jul 02 2025
%e A222134 2.791287847477920003294023596864...
%t A222134 RealDigits[(1 + Sqrt[21])/2, 10, 130]
%o A222134 (PARI) (sqrt(21) + 1)/2 \\ _Charles R Greathouse IV_, Feb 07 2025
%Y A222134 Cf. A090458, A107905, A222135, A015440.
%K A222134 nonn,cons,easy
%O A222134 1,1
%A A222134 _Jaroslav Krizek_, Feb 08 2013