A135005 - OEIS

%I #25 Apr 20 2023 04:22:28

%S 1,8,3,9,3,9,7,2,0,5,8,5,7,2,1,1,6,0,7,9,7,7,6,1,8,8,5,0,8,0,7,3,0,4,

%T 3,3,7,2,2,9,0,5,5,6,5,5,1,5,8,8,3,9,1,7,2,5,3,9,1,8,4,0,0,8,4,8,7,3,

%U 0,7,4,7,8,7,2,4,4,9,9,0,1,6,7,8,5,7,3,6,3,7,1,7,2,9,5,9,8,2,1,8,7,3,3,1,3,6,6,2,6

%N Decimal expansion of 5/e.

%C The fraction of substituents which become isolated in a simple polymer model is 1/10 this number, see Flory 1939 (and 1936). - _Charles R Greathouse IV_, Nov 30 2012

%H G. C. Greubel, <a href="/A135005/b135005.txt">Table of n, a(n) for n = 1..2000</a>

%H Paul J. Flory, <a href="http://dx.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 Paul J. Flory, <a href="http://dx.doi.org/10.1021/ja01301a016">Molecular size distribution in linear condensation polymers</a>, Journal of the American Chemical Society 58:10 (1936), pp. 1877-1885.

%H Ovidiu Furdui, <a href="https://austms.org.au/wp-content/uploads/Gazette/2008/Nov08/Gazette35(5)Web.pdf#page=49">From Lalescu's sequence to a Gamma function limit</a>, Gazette of the Australian Mathematical Society, Vol. 35, No. 5 (2008), pp. 339-344.

%F Equals 5/A001113 and 5*A068985. - _Michel Marcus_, Sep 17 2016

%F 1/(2*e) = Integral_{x=1..oo} e^(-x^2) * x dx. - _Amiram Eldar_, Aug 03 2020

%F 1/(2*e) = lim_{n->oo} n * ((n+1)!^(1/(n+1)) - n!^(1/n) - 1/e) (Furdui, 2008). - _Amiram Eldar_, Apr 20 2023

%e 5/e = 1.839397205857211607977618850807304337229...

%e 1/(2*e) = 0.1839397205857211607977618850807304337229... (see Greathouse's comment).

%t RealDigits[5/E , 10, 50][[1]] (* _G. C. Greubel_, Sep 16 2016 *)

%o (PARI) 5/exp(1) \\ _Michel Marcus_, Sep 17 2016

%Y Cf. A001113, A068985.

%K cons,nonn

%O 1,2

%A _Omar E. Pol_, Nov 15 2007