A130011 - OEIS

%I #32 Apr 17 2016 08:56:55

%S 1,4,5,12,15,16,17,18,19,20,21,36,37,38,45,48,51,54,57,60,63,64,65,66,

%T 67,68,69

%N A self-describing sequence. Pick any integer n in the sequence; this n says: "There are n terms in the sequence that are <= 3n". This sequence is the slowest increasing one with this property.

%C See comments in A094591 and A037988.

%C It is not clear in what sense "slowest increasing" is meant in the description of this sequence. The definition requires that there be exactly a(k) terms <= 3 a(k), for any index k. Therefore, a(n+1) > 3n for all indices n of the form n = a(k). Thus, any such sequence has an infinite number of terms a(k) >= 3k-2. The lexicographically first variant A260107, which starts (1, 4, 5, 6, 13, 16, 19, 20, 21, 22, ...), also has all its terms a(k) <= 3k-2, so it cannot be said to increase faster. - _M. F. Hasler_, Jul 16 2015

%H <a href="/A130011/b130011.txt">Table of n, a(n) for n = 1..27</a>

%K more,nonn

%O 1,2

%A _Eric Angelini_, Jun 15 2007