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A055170 n-th distinct number to appear in A055168; also the n-th to appear in A217760.

%I A055170 #20 Oct 17 2017 09:27:30
%S A055170 0,1,2,3,4,5,6,9,7,11,8,13,17,10,19,21,15,12,23,26,20,14,16,28,22,32,
%T A055170 24,35,27,18,38,30,25,41,34,29,44,31,48,50,46,36,52,39,42,56,37,60,54,
%U A055170 47,33,63,58,40,43,68,53,45,72,65,76,55,61,51
%N A055170 n-th distinct number to appear in A055168; also the n-th to appear in A217760.
%C A055170 Conjecture: this sequence is a permutation of the nonnegative integers.
%C A055170 This is the limiting sequence of the noun-integers in the n-th segment generated as in A217760 (but not A055186); see Example.
%C A055170 The conjecture is true: the number 0 appears in every segment of A055168, and, for n > 0, n appears in the (n+1)-th segment (as the number of occurrences of 0 in the previous segments). - _Rémy Sigrist_, Oct 16 2017
%H A055170 Peter J. C. Moses, <a href="/A055170/b055170.txt">Table of n, a(n) for n = 1..6000</a>
%e A055170 Following the adjective-before-noun definition at A217760, the first segments are
%e A055170 0..1..2 1..3 3 1..4 5 2 2..5 6 5 3 1 1..6 9 6 5 2 4 1..
%e A055170 ...0..0 1..0 1 2..0 1 2 3..0 1 2 3 4 5..0 1 2 3 4 5 6..
%e A055170 (continuing:)
%e A055170 7 11 8 6 4 6 4 1....8 13 9 7 7 7 5 2 1 1..1
%e A055170 0..1 2 3 4 5 6 9....0..1 2 3 4 5 6 9 7 11 8,
%e A055170 this last segment counting the "8 0's and 13 1's and 9 2's..." which have previously appeared.  The numbers 8, 13, 9 are used as adjectives and the numbers 0 1 2 3 4 5 6 9 7 11 8 (as in A055170) are used as nouns.
%t A055170 s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ (DeleteDuplicates[s])}], {30}]; DeleteDuplicates[s] (* _Peter J. C. Moses_, Mar 25 2013 *)
%Y A055170 Cf. A055168, A217760.
%K A055170 nonn
%O A055170 1,3
%A A055170 _Clark Kimberling_, Apr 27 2000
%E A055170 Corrected and edited by _Clark Kimberling_, Oct 24 2009
%E A055170 Reconciled to A217760 (formerly A055186) by _Clark Kimberling_, Mar 25 2013