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 A320029 #36 Jul 02 2025 11:01:10
%S A320029 3,5,4,1,3,8,1,2,6,5,1,4,9,1,0,9,8,4,4,4,9,9,8,4,2,1,2,2,6,0,1,0,3,3,
%T A320029 5,3,1,0,4,2,4,8,5,0,4,7,3,9,3,2,0,5,5,9,3,2,0,9,5,7,6,5,2,3,2,4,3,1,
%U A320029 6,6,3,6,2,6,5,9,4,5,5,1,1,9,9,0,1,5,3,3,2,1,3,9,7,8,9,2,4,3,3,1,7,1,5,4,6
%N A320029 Decimal expansion of sqrt(9 + sqrt(9 + sqrt(9 + sqrt(9 + ...)))) = (sqrt(37) + 1)/2.
%C A320029 For x >= 0, sqrt(x + sqrt(x + sqrt(x + sqrt(x + ...)))) = (sqrt(4*x+1) + 1)/2. This is an integer for each x such that 2*x is a term in A000217.
%H A320029 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A320029 Minimal polynomial: x^2 - x - 9. - _Stefano Spezia_, Jul 02 2025
%e A320029 3.541381265149109844499842122601033531042485047393205593209576523243166362659...
%p A320029 evalf((sqrt(37)+1)/2,120); # _Muniru A Asiru_, Oct 07 2018
%t A320029 RealDigits[ Fold[ Sqrt[#1 + #2] &, 0, Table[9, {135}]], 10, 111][[1]] (* or *)
%t A320029 RealDigits[(Sqrt[37] + 1)/2, 10, 111][[1]]
%o A320029 (PARI) (sqrt(37)+1)/2 \\ _Altug Alkan_, Oct 03 2018
%Y A320029 Cf. A000007, A001622, A000038, A209927, A222132, A222134, A223140, A235162.
%K A320029 nonn,cons,easy
%O A320029 1,1
%A A320029 _Robert G. Wilson v_, Oct 03 2018