A077644 Number of decimal digits of A070177(n).

1, 2, 9, 32, 107, 347, 1108, 3515, 11132, 35219, 111391, 352269, 1113996, 3522791, 11140072, 35228031, 111400846, 352280442, 1114008610, 3522804578, 11140086260

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..20.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy] p. 825.

Fredrik Johansson, Efficient implementation of the Hardy-Ramanujan-Rademacher formula, 2012 preprint, to be published in LMS Journal of Computation and Mathematics.

Fredrik Johansson, New partition function record: p(10^20) computed (2014)

Herbert S. Wilf, Lectures on Integer Partitions

Formula

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

Example

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

Mathematica

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

Prog

(PARI) a(n)=#Str(numbpart(10^n)) \\ Charles R Greathouse IV, Jul 09 2012

Crossrefs

Cf. A070177.

Sequence in context: A332870 A074084 A053152 * A292482 A053369 A076959

Adjacent sequences: A077641 A077642 A077643 * A077645 A077646 A077647

Keyword

nonn,base,more

Author

Labos Elemer, Nov 15 2002

Extensions

a(0), a(10)-a(12), a(15)=35228031 from Robert G. Wilson v, Jun 08 2010

a(13)-a(19) from Charles R Greathouse IV, Jul 09 2012 based on Johansson 2012

a(20) from Robert G. Wilson v, Mar 02 2014

Status

approved