A077644 - OEIS

%I #28 May 08 2018 15:11:55

%S 1,2,9,32,107,347,1108,3515,11132,35219,111391,352269,1113996,3522791,

%T 11140072,35228031,111400846,352280442,1114008610,3522804578,

%U 11140086260

%N Number of decimal digits of A070177(n).

%D Richard P. Stanley, Enumerative Combinatorics, Cambridge University Press, April 1997, p. 79.

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy] p. 825.

%H Fredrik Johansson, <a href="http://arxiv.org/abs/1205.5991">Efficient implementation of the Hardy-Ramanujan-Rademacher formula</a>, 2012 preprint, to be published in LMS Journal of Computation and Mathematics.

%H Fredrik Johansson, <a href="http://fredrikj.net/blog/2014/03/new-partition-function-record/">New partition function record: p(10^20) computed</a> (2014)

%H Herbert S. Wilf, <a href="http://www.math.upenn.edu/~wilf/PIMS/PIMSLectures.pdf">Lectures on Integer Partitions</a>

%F a(n) = (Pi*sqrt(2/3)*sqrt(10)^n-log(48)/2-n*log(10))/log(10) + O(1). - _Charles R Greathouse IV_, Jul 10 2012

%e p(10^3) = 24061467864032622473692149727991 has 32 decimal digits, so a(3) = 32.

%t f[n_] := Floor[ Log[10, PartitionsP[10^n]] + 1]; Array[f, 13, 0]

%o (PARI) a(n)=#Str(numbpart(10^n)) \\ _Charles R Greathouse IV_, Jul 09 2012

%Y Cf. A070177.

%K nonn,base,more

%O 0,2

%A _Labos Elemer_, Nov 15 2002

%E a(0), a(10)-a(12), a(15)=35228031 from _Robert G. Wilson v_, Jun 08 2010

%E a(13)-a(19) from _Charles R Greathouse IV_, Jul 09 2012 based on Johansson 2012

%E a(20) from _Robert G. Wilson v_, Mar 02 2014