A055187 Cumulative counting sequence: method A (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, 1, 2, 3, 3, 2, 4, 1, 6, 11, 1, 3, 2, 5, 3, 3, 4, 2, 6, 1, 8, 13, 1, 5, 2, 8, 3, 4, 4, 1, 5, 3, 6, 2, 8, 1, 11, 16, 1, 7, 2, 10, 3, 6, 4, 3, 5, 4, 6, 4, 8, 2, 11, 1, 13, 18, 1, 9, 2, 12, 3, 9, 4, 4, 5, 6, 6, 1, 7, 5, 8, 1, 10, 3, 11, 2, 13, 1, 16, 22, 1

Offset

1,4

Comments

Conjectures: limit as n goes to infinity of max {a(k) : 1<=k<=n}/sqrt(n) = 2;

-3 < a(n) - 2*sqrt(n) < 3 for all n;

there are infinitely many n such that a(n)=a(n+1). - Benoit Cloitre, Jan 30 2003

After starting with 1, successive segments are generated in adjective-before-noun pairs as in A055186 (i.e., the noun-integers are in increasing order). See A217780 for the sequence originally placed here, in which the noun-integers are in order of 1st occurrence. - Clark Kimberling, Mar 24 2013

Links

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

Example

After writing 1, pairs, written vertically, are as shown:
1..1..3..4 1..6 2 1..8 1 3 2 1..
...1..1..1 3..1 3 4..1 2 3 4 6..

Mathematica

s = {1}; Do[s = Flatten[{s, {Count[s, #], #} & /@ Union[s]}], {14}]; s  (* A055187 *) (* Peter J. C. Moses, Mar 21 2013 *)

Crossrefs

Cf. A055186, A217780.

Sequence in context: A260510 A125291 A320640 * A217780 A329316 A109411

Adjacent sequences: A055184 A055185 A055186 * A055188 A055189 A055190

Keyword

nonn

Author

Clark Kimberling, Apr 27 2000

Extensions

Corrected and extended by Benoit Cloitre, Jan 30 2003

Status

approved