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 A219863 #37 Oct 02 2022 23:15:15 %S A219863 8,6,4,6,6,4,7,1,6,7,6,3,3,8,7,3,0,8,1,0,6,0,0,0,5,0,5,0,2,7,5,1,5,5, %T A219863 9,6,5,9,2,3,6,8,4,5,4,0,9,0,4,2,4,1,1,8,5,3,1,8,4,1,1,2,7,3,4,5,9,2, %U A219863 6,6,2,5,8,9,8,5,1,2,3,1,0,0,6,2,9,0,1,8,7,7,5,0,9,3,4,2,9,5,1,2 %N A219863 Decimal expansion of 1 - 1/e^2. %C A219863 Consider a substrate (such as polyvinyl alcohol or in forming the polymer of methyl vinyl ketone) in a "1,3 configuration" in which substituents branching off the substrate can irreversibly join with neighboring substituents unless the neighbor is already joined to its other neighbor. Then this constant is the fraction of unjoined substituents on an infinite substrate. %C A219863 This also applies to reversible reactions when the rate of forward reaction is much faster than that of backward reaction; see Flory p. 1518 footnote 5. This had "satisfactory accord" with his experimental data using methyl vinyl ketone polymer for which the experimentally-obtained percentage was 0.85. %C A219863 (A 1,k configuration is a substituent branching off a carbon atom, k-2 intermediate carbon atoms, and substituent branching off a carbon atom.) %C A219863 Solution of the discrete parking problem when infinite lattice randomly filled with 2-length segments. - _Philipp O. Tsvetkov_, Mar 27 2019 %D A219863 Pavel L. Krapivsky, Sidney Redner, and Eli Ben-Naim, A Kinetic View of Statistical Physics, Cambridge University Press, 2010. %H A219863 Paul J. Flory, <a href="https://doi.org/10.1021/ja01875a053">Intramolecular reaction between neighboring substituents of vinyl polymers</a>, Journal of the American Chemical Society 61:6 (1939), pp. 1518-1521. %H A219863 Philipp O. Tsvetkov, <a href="https://doi.org/10.1038/s41598-020-77896-0">Stoichiometry of irreversible ligand binding to a one-dimensional lattice</a>, Scientific Reports, Springer Nature (2020) Vol. 10, Article number: 21308. %H A219863 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A219863 Equals 2*A247847. - _Philipp O. Tsvetkov_, Mar 27 2019 %e A219863 0.8646647167633873081060005... %t A219863 RealDigits[1 - E^(-2), 10, 105][[1]] (* _Alonso del Arte_, Dec 04 2012 *) %o A219863 (PARI) 1-exp(-2) %Y A219863 Cf. A092553, A013301, A247847. %K A219863 nonn,cons %O A219863 0,1 %A A219863 _Charles R Greathouse IV_, Nov 30 2012