login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A295866 Number of decimal digits in the number of partitions of n. 0
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

In his book on analytic number theory, Don Newman tells this amusing story regarding the number of digits in p(n): "This is told of Major MacMahon who kept a list of these partition numbers arranged one under another up into the hundreds. It suddenly occurred to him that, viewed from a distance, the outline of the digits seemed to form a parabola! Thus the number of digits in p(n), the number of partitions of n, is around C*sqrt(n), or p(n) itself is very roughly e^(a*sqrt(n)). The first crude assessment of p(n)!"

REFERENCES

D. J. Newman, Analytic number theory, Springer Verlag, 1998, p. 17.

LINKS

Table of n, a(n) for n=0..86.

FORMULA

a(n) = A055642(A000041(n)).

MATHEMATICA

Join[{1}, IntegerLength[PartitionsP[#]] & /@ Range[99]]

PROG

(PARI) a(n) = #digits(numbpart(n)); \\ Michel Marcus, Feb 17 2018

CROSSREFS

Cf. A000041, A055642, A072212, A097985.

Sequence in context: A204164 A257639 A180447 * A115338 A226046 A133877

Adjacent sequences:  A295863 A295864 A295865 * A295867 A295868 A295869

KEYWORD

nonn,base

AUTHOR

José Hernández, Feb 13 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 17:36 EDT 2020. Contains 334595 sequences. (Running on oeis4.)