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A055171 Cumulative counting sequence: method B (noun,adjective)-pairs with first term 1.

%I A055171 #27 Jan 21 2025 14:33:14
%S A055171 1,1,1,1,3,1,4,3,1,1,6,3,2,4,1,1,8,3,3,4,2,6,1,2,1,1,11,3,5,4,3,6,2,2,
%T A055171 3,8,1,1,13,3,8,4,4,6,3,2,5,8,2,11,1,5,1,1,16,3,10,4,6,6,4,2,7,8,4,11,
%U A055171 2,5,3,13,1,1,18,3,12,4,9,6,6,2,9,8,5,11,3,5
%N A055171 Cumulative counting sequence: method B (noun,adjective)-pairs with first term 1.
%C A055171 Segments (generated as at A055168):  1; 1,1; 1,3; 1,4,3,1; 1,6,3,2,4,1; ...
%C A055171 Conjecture: every positive integer occurs.
%H A055171 Seiichi Manyama, <a href="/A055171/b055171.txt">Table of n, a(n) for n = 1..10000</a>
%e A055171 Write 1, thus having 1 once, thus having 1 3 times, thus having 1 4 times and 3 once, etc.
%t A055171 s = {1}; Do[s = Flatten[{s, {#,Count[s, #]} & /@ DeleteDuplicates[s]}], {24}]; s (* _Peter J. C. Moses_, Mar 21 2013 *)
%o A055171 (Python)
%o A055171 from collections import Counter
%o A055171 from sympy import flatten
%o A055171 t = [1]
%o A055171 [t.extend(flatten(Counter(t).items())) for _ in range(10)]
%o A055171 print(t) # _Nicholas Stefan Georgescu_, Jan 16 2025
%Y A055171 Cf. A055168.
%K A055171 nonn
%O A055171 1,5
%A A055171 _Clark Kimberling_, Apr 27 2000