

A181157


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.


5



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, 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, 1, 2, 1, 35, 1, 12, 1, 2, 1, 5, 1, 3, 1, 2, 1, 11, 1, 4, 1, 2, 1, 8, 1, 3
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OFFSET

1,2


COMMENTS

a(n) = 1 when n mod 2 = 1.
a(n) = 2 when n mod 6 = 2.
a(n) = 3 when n mod 12 = 6.
a(n) = 4 when n mod 60 = 4, 24 or 48.
a(n) = 5 when n mod 60 = 16 or 40.
Otherwise a(n) >= 6.
When we pick a term from this sequence at random, the expectation diverges to infinity.


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000


EXAMPLE

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.
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.


MATHEMATICA

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 *)


CROSSREFS

Cf. A181158 (records), A181159 (first occurrence of n).
Sequence in context: A243792 A124331 A242885 * A095248 A122458 A329644
Adjacent sequences: A181154 A181155 A181156 * A181158 A181159 A181160


KEYWORD

nonn


AUTHOR

Keisuke Sato (st(AT)r3z.org), Oct 07 2010


EXTENSIONS

a(61)a(90) added from bfile by Charlie Neder, Feb 08 2019


STATUS

approved



