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

Author

José Hernández, Feb 13 2018

Keywords

• nonn
• base

Links

• 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

Crossrefs

Cf. A000030, A000041, A178743.

Programs

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 *)

PARI

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

Formula

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