cp's OEIS Frontend

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.

A246952 Decimal expansion of sigma, a constant appearing in the asymptotic expression of the number a(n) of Carlitz compositions of size n.

This page as a plain text file.
%I A246952 #12 Jan 17 2020 16:14:20
%S A246952 5,7,1,3,4,9,7,9,3,1,5,8,0,8,7,6,4,3,1,1,2,2,1,7,9,0,4,8,9,1,9,7,4,6,
%T A246952 0,0,3,3,6,1,7,6,2,2,4,9,3,7,5,3,4,1,4,5,1,1,7,1,8,1,8,5,8,7,9,4,2,7,
%U A246952 4,6,2,8,6,5,6,8,6,6,8,9,8,8,7,3,8,4,8,5,3,0,9,7,1,9,3,4,3,7,5,7,6,3,5
%N A246952 Decimal expansion of sigma, a constant appearing in the asymptotic expression of the number a(n) of Carlitz compositions of size n.
%H A246952 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 38.
%H A246952 A. Knopfmacher and H. Prodinger, <a href="http://dx.doi.org/10.1006/eujc.1998.0216">On Carlitz compositions</a>, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.
%F A246952 Sigma is the unique solution of the equation F(x)=1, 0 <= x <= 1, where F(x) = sum_{j>=1} (-1)^(j - 1)*(x^j/(1 - x^j)).
%F A246952 a(n) ~ 1/(sigma*F'(sigma))*(1/sigma)^n = c*r^n, where c = 0.456387... and r = A241902 = 1.750243...
%e A246952 0.571349793158087643112217904891974600336176224937534145...
%t A246952 digits = 103; F[x_?NumericQ] := NSum[(-1)^(j - 1)*(x^j/(1 - x^j)), {j, 1, Infinity}, WorkingPrecision -> digits+5]; sigma = x /. FindRoot[F[x] == 1, {x, 2/5, 1/2}, WorkingPrecision -> digits+5]; RealDigits[sigma, 10, digits] // First
%Y A246952 Cf. A003242, A241902.
%K A246952 nonn,cons
%O A246952 0,1
%A A246952 _Jean-François Alcover_, Sep 08 2014