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A295868 Initial digit of the number of partitions of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 21:15 EDT 2019. Contains 327282 sequences. (Running on oeis4.)