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%I #37 Mar 04 2018 19:49:49
%S 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,
%T 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,
%U 7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8
%N Number of decimal digits in the number of partitions of n.
%C 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 D. J. Newman, Analytic number theory, Springer Verlag, 1998, p. 17.
%F a(n) = A055642(A000041(n)).
%t Join[{1}, IntegerLength[PartitionsP[#]] & /@ Range[99]]
%o (PARI) a(n) = #digits(numbpart(n)); \\ _Michel Marcus_, Feb 17 2018
%Y Cf. A000041, A055642, A072212, A097985.
%K nonn,base
%O 0,7
%A _José Hernández_, Feb 13 2018