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A295868 Initial digit of the number of partitions of n. 0

%I

%S 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,

%T 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,

%U 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

%N Initial digit of the number of partitions of n.

%H Theresa C. Anderson, Larry Rolen and Ruth Stoehr, <a href="https://doi.org/10.1090/S0002-9939-2010-10577-4">Benford's Law for Coefficients of Modular Forms and Partition Functions</a>, Proceedings of the American Mathematical Society, 139 (2011), pp. 1533-1541.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Benford%27s_law">Benford's law</a>

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

%t (* The first one hundred terms of the sequence *)

%t Join[{1}, First[IntegerDigits[PartitionsP[#]]] & /@ Range[99]]

%t f[n_] := Block[{p = PartitionsP@ n}, Floor[p/10^Floor@ Log10@ p]]; Array[f, 105, 0] (* _Robert G. Wilson v_, Feb 18 2018 *)

%o (PARI) a(n) = digits(numbpart(n))[1]; \\ _Michel Marcus_, Feb 16 2018

%Y Cf. A000030, A000041, A178743.

%K nonn,base

%O 0,3

%A _José Hernández_, Feb 13 2018

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Last modified July 30 19:33 EDT 2021. Contains 346359 sequences. (Running on oeis4.)