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Cumulative counting sequence: (adjective-before-noun) pairs with first term 1.
7

%I #17 Nov 11 2022 13:16:45

%S 1,1,1,3,1,4,1,1,3,6,1,2,3,1,4,8,1,3,3,2,4,1,6,1,2,11,1,5,3,3,4,2,6,3,

%T 2,1,8,13,1,8,3,4,4,3,6,5,2,2,8,1,11,1,5,16,1,10,3,6,4,4,6,7,2,4,8,2,

%U 11,3,5,1,13,18,1,12,3,9,4,6,6,9,2,5,8,3,11,4,5,2,13,1,16,1,10,1,7

%N Cumulative counting sequence: (adjective-before-noun) pairs with first term 1.

%C After starting with 1, successive segments are generated in adjective-before-noun pairs as in A217760, not as in A055187. That is, noun-integers occur in order of 1st appearance, not increasing order.

%H Seiichi Manyama, <a href="/A217780/b217780.txt">Table of n, a(n) for n = 1..10000</a>

%e Writing pairs vertically, the initial segments are

%e 1..1..3..4 1..6 2 1..8 3 2 1 1..11 5 3 2 3 1

%e ...1..1..1 3..1 3 4..1 3 4 6 2...1 3 4 6 2 8.

%e The 5th segment is read "6 1's and 2 3's and 1 4," this being a count of all the previously written numbers. The numbers 6,2,1 are used as adjectives, whereas 1,3,4 are used as nouns. Here, the nouns are kept in order of first appearance; in A055187, they are in increasing order. - _Clark Kimberling_, Mar 25 2013

%t s = {1}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s (* _Peter J. C. Moses_, Mar 21 2013 *)

%Y Cf. A217760, A055187.

%K nonn,easy

%O 1,4

%A _Clark Kimberling_, Mar 25 2013

%E More terms from _Seiichi Manyama_, Nov 10 2022