A072212 -id:A072212 - cp's OEIS frontend

A097985 Number of partition numbers with n digits.

5, 7, 9, 11, 13, 15, 16, 18, 20, 21, 24, 25, 26, 29, 30, 32, 33, 35, 37, 38, 41, 41, 44, 45, 47, 48, 50, 52, 54, 55, 56, 59, 60, 62, 63, 65, 67, 68, 70, 71, 74, 74, 77, 78, 80, 81, 83, 85, 86, 88, 90, 91, 93, 95, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 112, 114, 116

Offset: 1

Lekraj Beedassy, Sep 07 2004

a(n)=A072212(n)-A072212(n-1) for n>=2. - Emeric Deutsch, Mar 19 2005

			a(2)=7 because the number of partitions of 5,6,...,13 are 7,11,15,22,30,42,56, 77,101 and thus exactly 7 partition numbers have 2 digits.

Cf. A000041, A072212.

Corrected and extended by Emeric Deutsch, Mar 19 2005

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

Original entry on oeis.org

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

José Hernández, Feb 13 2018

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)!"

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

Cf. A000041, A055642, A072212, A097985.

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

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

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

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A097985 Number of partition numbers with n digits.

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

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