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

Author

Clark Kimberling, Apr 27 2000

Keywords

• nonn

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

Examples

			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..
		

Links

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

Crossrefs

Cf. A055186, A217780.

Programs

Mathematica

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

Extensions

Corrected and extended by Benoit Cloitre, Jan 30 2003