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%I #9 Feb 09 2019 15:07:29
%S 1,2,1,4,1,3,1,2,1,10,1,6,1,2,1,5,1,3,1,2,1,22,1,4,1,2,1,9,1,3,1,2,1,
%T 8,1,7,1,2,1,5,1,3,1,2,1,46,1,4,1,2,1,17,1,3,1,2,1,14,1,6,1,2,1,4,1,3,
%U 1,2,1,35,1,12,1,2,1,5,1,3,1,2,1,11,1,4,1,2,1,8,1,3
%N a(n) is the greatest integer such that the occurrence rate of integers k and above in {a(1), ..., a(n)} <= 1/k for all positive integers k.
%C a(n) = 1 when n mod 2 = 1.
%C a(n) = 2 when n mod 6 = 2.
%C a(n) = 3 when n mod 12 = 6.
%C a(n) = 4 when n mod 60 = 4, 24 or 48.
%C a(n) = 5 when n mod 60 = 16 or 40.
%C Otherwise a(n) >= 6.
%C When we pick a term from this sequence at random, the expectation diverges to infinity.
%H Ivan Neretin, <a href="/A181157/b181157.txt">Table of n, a(n) for n = 1..10000</a>
%e Let denote the occurrence rate of integers k and above in {a(1), ..., a(n)} as r(n,k). For example, r(5,2) = 2/5 since {a(1), ..., a(5)} = {1, 2, 1, 4, 1}: integers 2 and above occur twice in them.
%e a(6) can be 3 or above since r(6,1) = 6/6 <= 1/1, r(6,2) = 3/6 <= 1/2, and r(6,3) = 2/6 <= 1/3. But if a(6) >= 4, then r(6,4) = 2/6 > 1/4. Thus a(6) cannot be greater than 3, therefore a(6) = 3.
%t mx = 60; acc = ConstantArray[0, mx + 1]; a = {}; Do[AppendTo[a, k = Min[Select[Range[mx], n/# - acc[[#]] < 1 &]] - 1]; acc[[Range[k]]]++, {n, mx}]; a (* _Ivan Neretin_, May 20 2015 *)
%Y Cf. A181158 (records), A181159 (first occurrence of n).
%K nonn
%O 1,2
%A Keisuke Sato (st(AT)r3z.org), Oct 07 2010
%E a(61)-a(90) added from b-file by _Charlie Neder_, Feb 08 2019
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