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 A249023 #13 Jun 15 2025 01:32:07
%S A249023 9,9,4,3,2,2,8,7,4,7,3,3,4,6,3,9,2,8,0,8,1,5,9,8,0
%N A249023 Decimal expansion of Tangent Euler constant.
%C A249023 The Tangent-Euler constant is introduced here as the limit as n increases without bound of Sum_{k=1..n} tan(1/k) - Integral_{x=1..n} tan(1/x) dx; this is analogous to the Euler constant, defined as the limit of Sum_{k=1..n} 1/k - Integral_{x=1..n} 1/x dx.
%e A249023 Tangent Euler constant = 0.9943228747334639280815980...
%t A249023 CI = N[Integrate[Normal[Series[Tan[x], {x, 0, 500}]] /. x -> 1/x, x] /. x -> 1, 100]; t = (Total[Table[((-1)^(n - 1) 2^(2 n) (2^(2 n) - 1) BernoulliB[2 n])/(2 n)! HarmonicNumber[k, 2 n - 1], {n, 80}]] /. k -> #) - (N[Integrate[Normal[Series[Tan[x], {x, 0, 10}]] /. x -> 1/x, x] /. x -> #, 100] - CI) &[N[10^30, 30]]
%t A249023 RealDigits[t][[1]]
%t A249023 (* _Peter J. C. Moses_, Oct 20 2014 *)
%Y A249023 Cf. A001620 (Euler constant), A249022 (Sine Euler constant).
%K A249023 nonn,cons,more
%O A249023 0,1
%A A249023 _Clark Kimberling_, Oct 22 2014