This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A176015 #43 Mar 05 2025 07:24:13
%S A176015 1,1,7,0,8,2,0,3,9,3,2,4,9,9,3,6,9,0,8,9,2,2,7,5,2,1,0,0,6,1,9,3,8,2,
%T A176015 8,7,0,6,3,2,1,8,5,5,0,7,8,8,3,4,5,7,7,1,7,2,8,1,2,6,9,1,7,3,6,2,3,1,
%U A176015 5,6,2,7,7,6,9,1,3,4,1,4,6,9,8,2,4,3,2,4,3,2,2,5,1,3,6,3,4,6,8,2,4,9,0,8,5
%N A176015 Decimal expansion of (5 + 3*sqrt(5))/10.
%C A176015 Continued fraction expansion of (5 + 3*sqrt(5))/10 is A010686.
%C A176015 The horizontal distance between the accumulation point and the outermost point of a golden spiral inscribed inside a golden rectangle with dimensions phi and 1 along the x and y axes, respectively (the vertical distance is A244847). - _Amiram Eldar_, May 18 2021
%D A176015 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.2 The Golden Mean, phi, p. 7.
%H A176015 Muniru A Asiru, <a href="/A176015/b176015.txt">Table of n, a(n) for n = 1..1000</a> [a(1000) corrected by _Georg Fischer_, Apr 02 2020]
%H A176015 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A176015 Equals (A134976 + 8)/10. - _R. J. Mathar_, Apr 12 2010
%F A176015 From _Arkadiusz Wesolowski_, Jan 07 2018: (Start)
%F A176015 Equals A001622^2 / sqrt(5).
%F A176015 Equals lim_{n -> infinity} A000045(n+2) / A001622^n. (End)
%F A176015 Equals 1/A090550 + 1. - _Michel Marcus_, Apr 20 2020
%F A176015 Minimal polynomial is 5x^2 - 5x - 1 (this number is an algebraic number but not an algebraic integer). - _Alonso del Arte_, Apr 20 2020
%F A176015 Equals lim_{k->oo} Fibonacci(k+2)/Lucas(k). - _Amiram Eldar_, Feb 06 2022
%e A176015 (5 + 3*sqrt(5))/10 = 1.17082039324993690892...
%p A176015 Digits := 1000: (5+3*sqrt(5.0))/10; # _Muniru A Asiru_, Jan 22 2018
%t A176015 RealDigits[(5 + 3 Sqrt[5])/10, 10, 1001][[1]] (* _Georg Fischer_, Apr 02 2020 *)
%o A176015 (Magma) SetDefaultRealField(RealField(105)); n:=(5+3*Sqrt(5))/10; Reverse(Intseq(Floor(10^104*n))); // _Arkadiusz Wesolowski_, Jan 07 2018
%o A176015 (PARI) (5 + 3*sqrt(5))/10 \\ _Michel Marcus_, Apr 20 2020
%Y A176015 Cf. A000032, A000045, A001622, A002163 (decimal expansion of sqrt(5)), A010686 (repeat 1, 5), A090550, A134976.
%Y A176015 Cf. A010499 (decimal expansion of 3*sqrt(5)).
%K A176015 cons,nonn
%O A176015 1,3
%A A176015 _Klaus Brockhaus_, Apr 06 2010