A295866 Number of decimal digits in the number of partitions of n.

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

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 A348522 A226046

Adjacent sequences: A295863 A295864 A295865 * A295867 A295868 A295869

Keyword

nonn,base

Author

José Hernández, Feb 13 2018

Status

approved