A295868 Initial digit of the number of partitions of n.

1, 1, 2, 3, 5, 7, 1, 1, 2, 3, 4, 5, 7, 1, 1, 1, 2, 2, 3, 4, 6, 7, 1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 8, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1

Offset

0,3

Links

Table of n, a(n) for n=0..99.

Theresa C. Anderson, Larry Rolen and Ruth Stoehr, Benford's Law for Coefficients of Modular Forms and Partition Functions, Proceedings of the American Mathematical Society, 139 (2011), pp. 1533-1541.

Wikipedia, Benford's law

Formula

a(n) = A000030(A000041(n)).

Mathematica

(* The first one hundred terms of the sequence *)
Join[{1}, First[IntegerDigits[PartitionsP[#]]] & /@ Range[99]]
f[n_] := Block[{p = PartitionsP@ n}, Floor[p/10^Floor@ Log10@ p]]; Array[f, 105, 0] (* Robert G. Wilson v, Feb 18 2018 *)

Prog

(PARI) a(n) = digits(numbpart(n))[1]; \\ Michel Marcus, Feb 16 2018

Crossrefs

Cf. A000030, A000041, A178743.

Sequence in context: A077648 A033308 A134690 * A228355 A065859 A258062

Adjacent sequences: A295865 A295866 A295867 * A295869 A295870 A295871

Keyword

nonn,base

Author

José Hernández, Feb 13 2018

Status

approved