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 A255272 #23 Feb 16 2025 08:33:25
%S A255272 7,7,2,5,2,5,1,8,3,6,9,3,7,7,0,7,1,6,4,1,9,5,0,6,8,9,3,3,0,6,2,9,8,6,
%T A255272 6,2,6,3,7,8,1,5,9,3,0,4,6,1,0,7,9,1,1,8,6,6,4,9,3,2,8,2,1,6,7,2,9,6,
%U A255272 4,5,0,0,1,6,8,2,6,8,8,8,1,6,1,8,4,5,0,4,8,4,5,7,4,0,6,9,5,7,8,6,9,7
%N A255272 Decimal expansion of the second smallest positive root of tan(x) = x.
%C A255272 This constant is quite close to 5*Pi/2 - 1/8 = 7.72898...
%C A255272 Searching for solutions x=k*Pi+Pi/2-e and small e, for k=1,2,3.... means via the approximation tan(x) = 1/e-e/3-e^3/45... that e is approximately 1/(k*Pi+Pi/2), so the constants x are close to k*Pi+Pi/2-1/(k*Pi+Pi/2). Here k=2 and the constant is close to 5*Pi/2-2/(5*Pi) = 7.7266576... - _R. J. Mathar_, Jul 11 2024
%H A255272 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/duBois-ReymondConstants.html">du Bois-Reymond Constants</a>.
%e A255272 7.72525183693770716419506893306298662637815930461...
%t A255272 xi[n_] := x /. FindRoot[Tan[x] == x, {x, n*Pi + Pi/2 - 1/(4*n)}, WorkingPrecision -> 102]; RealDigits[xi[2]] // First
%o A255272 (PARI) solve(x=7,7.8,tan(x)-x) \\ _Charles R Greathouse IV_, Apr 20 2016
%Y A255272 Cf. A115365 (smallest positive root), A062546 (C_2 = 2nd du Bois-Reymond constant), A224196 (C_3), A207528 (C_4), A243108 (C_5), A245333 (C_6).
%Y A255272 Cf. A079330, A088989.
%K A255272 nonn,cons,easy
%O A255272 1,1
%A A255272 _Jean-François Alcover_, Feb 20 2015