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The current definition does not exclude 1,2,2,4,... except for the claim that 3 is the unique integer that satisfies the conditions. See the comment in
oeis:A001462 for the correct understanding.
Penguian (
talk)
07:44, 5 November 2011 (UTC)reply
Not so. It “is a non-decreasing integer sequence where an is the number of times that n occurs in the sequence, starting with a1 = 1”. Since it's non-decreasing and a1 = 1, every integer n > 1 has an ≥ 1. Therefore, since an is the number of times that n occurs in the sequence, every integer n > 1 must appear, and since it's a non-decreasing sequence they must appear in order. That can be extended into a proof of uniqueness and existence by showing that for n > 2 we have an > n.
95.21.126.151 (
talk)
06:41, 20 September 2012 (UTC)reply