

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
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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



