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

1,4

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.

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A217760, A055187.

Sequence in context: A125291 A320640 A055187 * A329316 A109411 A302240

Adjacent sequences: A217777 A217778 A217779 * A217781 A217782 A217783

Keyword

nonn,easy

Author

Clark Kimberling, Mar 25 2013

Extensions

More terms from Seiichi Manyama, Nov 10 2022

Status

approved