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Integer part of log(n)^2.
0

%I #12 Nov 01 2024 02:02:07

%S 0,0,1,1,2,3,3,4,4,5,5,6,6,6,7,7,8,8,8,8,9,9,9,10,10,10,10,11,11,11,

%T 11,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,

%U 15,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,18,18

%N Integer part of log(n)^2.

%C Limit_{n->oo} Prime(n) = n*log(n).

%C Limit_{n->oo} PrimePi(n) = n/log(n).

%C Then ratio lengths are:

%C Limit_{n->oo} Prime(n)/PrimePi(n) = n*log(n)/(n/log(n)) = log(n)^2.

%F a(n) = floor(log(n)^2).

%t Table[Floor[Log[n]^2], {n, 1, 100}]

%Y Cf. A111114.

%K nonn,easy

%O 0,5

%A _Roger L. Bagula_, Mar 21 2013