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A077644 Number of decimal digits of A070177(n). 5
1, 2, 9, 32, 107, 347, 1108, 3515, 11132, 35219, 111391, 352269, 1113996, 3522791, 11140072, 35228031, 111400846, 352280442, 1114008610, 3522804578, 11140086260 (list; graph; refs; listen; history; text; internal format)
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: A082114 A074084 A053152 * A053369 A076959 A003697

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

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Last modified September 26 10:31 EDT 2017. Contains 292518 sequences.