

A092553


Decimal expansion of 1/e^2.


8



1, 3, 5, 3, 3, 5, 2, 8, 3, 2, 3, 6, 6, 1, 2, 6, 9, 1, 8, 9, 3, 9, 9, 9, 4, 9, 4, 9, 7, 2, 4, 8, 4, 4, 0, 3, 4, 0, 7, 6, 3, 1, 5, 4, 5, 9, 0, 9, 5, 7, 5, 8, 8, 1, 4, 6, 8, 1, 5, 8, 8, 7, 2, 6, 5, 4, 0, 7, 3, 3, 7, 4, 1, 0, 1, 4, 8, 7, 6, 8, 9, 9, 3, 7, 0, 9, 8, 1, 2, 2, 4, 9, 0, 6, 5, 7, 0, 4, 8, 7, 5, 5, 0, 7, 7
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OFFSET

0,2


COMMENTS

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 joined substituents on an infinite substrate.
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 experimentallyobtained percentage was 0.15.
(A 1,k configuration is a substituent branching off a carbon atom, k2 intermediate carbon atoms, and substituent branching off a carbon atom.)  Charles R Greathouse IV, Nov 30 2012
Also the probability, as n increases without bound, that a permutation of length n is simple: no intervals of length 1 < k < n (an interval of a permutation s is a set of contiguous numbers which in s have consecutive indices).  Charles R Greathouse IV, May 14 2014


LINKS

Table of n, a(n) for n=0..104.
M. H. Albert, M. D. Atkinson and M. Klazar, The enumeration of simple permutations, J. Integer Seq. 6 (2003) 03.4.4. arXiv:math/0304213.
R. Brignall, A survey of simple permutations, Permutation Patterns, ed. S. Linton, N. Ruškuc and V. Vatter, Cambridge Univ. Press, 2010, pp. 41—65; arXiv:0801.0963.
Paul J. Flory, Intramolecular reaction between neighboring substituents of vinyl polymers, Journal of the American Chemical Society 61:6 (1939), pp. 15181521.


EXAMPLE

0.1353352832366...


MATHEMATICA

RealDigits[N[1/E^2, 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)


PROG

(PARI) exp(2) \\ Charles R Greathouse IV, Nov 30 2012


CROSSREFS

Cf. A019774, A001113, A068985, A219863.
Sequence in context: A251754 A225581 A275391 * A112755 A239278 A284721
Adjacent sequences: A092550 A092551 A092552 * A092554 A092555 A092556


KEYWORD

cons,nonn


AUTHOR

Mohammad K. Azarian, Apr 09 2004


STATUS

approved



