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Decimal expansion of log(2) + 1/3.
1

%I #29 May 15 2019 12:42:07

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

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

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

%N Decimal expansion of log(2) + 1/3.

%C Given a Poisson distribution with parameter lambda, the median of the distribution is between lambda - log(2) and lambda + 1/3 (both sharp). This constant gives the width of this interval. Note that log(2) + 1/3 >= 1 so there is always at least one integer in the range.

%H K. P. Choi, <a href="http://dx.doi.org/10.1090/S0002-9939-1994-1195477-8">On the medians of gamma distributions and an equation of Ramanujan</a>, Proceedings of the American Mathematical Society 121:1 (May, 1994), pp. 245-251.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 1.026480513893278642...

%t RealDigits[Log[2] + 1/3, 10, 100] [[1]] (* _Vincenzo Librandi_, Jun 25 2015 *)

%o (PARI) log(2)+1/3

%Y Cf. A100045.

%K nonn,cons

%O 1,3

%A _Charles R Greathouse IV_, Jun 24 2015