login
A055187
Cumulative counting sequence: method A (adjective-before-noun)-pairs with first term 1.
6
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
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
Sequence in context: A260510 A125291 A320640 * A217780 A329316 A109411
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 27 2000
EXTENSIONS
Corrected and extended by Benoit Cloitre, Jan 30 2003
STATUS
approved