A217780 Cumulative counting sequence: (adjective-before-noun) pairs with first term 1.

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, 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, 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

Offset: 1

Author

Clark Kimberling, Mar 25 2013

Keywords

• nonn
• easy

Comments

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.

Examples

			Writing pairs vertically, the initial segments are
1..1..3..4 1..6 2 1..8 3 2 1 1..11 5 3 2 3 1
...1..1..1 3..1 3 4..1 3 4 6 2...1 3 4 6 2 8.
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
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A217760, A055187.

Programs

Mathematica

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

Extensions

More terms from Seiichi Manyama, Nov 10 2022