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A055186 Cumulative counting sequence: method A (adjective-before-noun)-pairs with first term 0. 8
0, 1, 0, 2, 0, 1, 1, 3, 0, 3, 1, 1, 2, 4, 0, 5, 1, 2, 2, 2, 3, 5, 0, 6, 1, 5, 2, 3, 3, 1, 4, 1, 5, 6, 0, 9, 1, 6, 2, 5, 3, 2, 4, 4, 5, 1, 6, 7, 0, 11, 1, 8, 2, 6, 3, 4, 4, 6, 5, 4, 6, 0, 7, 0, 8, 1, 9, 10, 0, 13, 1, 9, 2, 7, 3, 7, 4, 7, 5, 7, 6, 2, 7, 2, 8, 2, 9, 0, 10, 1, 11, 12, 0, 15, 1, 13, 2, 8, 3, 8, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Start with 0; at n-th step, write down what is in the sequence so far.

"Look and Say" how many times each integer (in increasing order), <= max {existing terms} appears in the sequence. Then concatenate.  Sequence's graph looks roughly like that of A080096.

For the original version, where "increasing order..." is "order of 1st appearance", see A217760.  The conjecture formerly placed here applies to A217760. - Clark Kimberling, Mar 24 2013

LINKS

Zak Seidov, Table of n, a(n) for n = 1..1019 (the first 22 steps)

FORMULA

Conjectures: a(n) < 2*sqrt(n); limit as n goes to infinity Max( a(k) : 1<=k<=n)/sqrt(n) exist = 2 - Benoit Cloitre, Jan 28 2003

EXAMPLE

Write 0, thus having 1 0, thus having 2 0's and 1 1, thus having 3 0's and 3 1's and 1 2, etc. 0; 1,0; 2,0,1,1; 3,0,3,1,1,2; ...

MATHEMATICA

s={0}; Do[ta=Table[{Count[s, # ], # }&/@Range[0, Max[s]]]; s=Flatten[{s, ta}], {22}]; s - Zak Seidov, Oct 23 2009

CROSSREFS

Cf. A005150. For other versions see A051120, A079668, A079686.

Cf. A055168-A055185 (method B) and A055187-A055191 (method A).

Cf. A217760.

Sequence in context: A135830 A029353 A064922 * A217760 A263412 A124035

Adjacent sequences:  A055183 A055184 A055185 * A055187 A055188 A055189

KEYWORD

nonn,base

AUTHOR

Clark Kimberling, Apr 27 2000

EXTENSIONS

Edited by N. J. A. Sloane, Jan 17 2009 at the suggestion of R. J. Mathar

Removed a conjecture. - Clark Kimberling, Oct 24 2009

Entries changed to match b-file. - N. J. A. Sloane, Oct 04 2010

STATUS

approved

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Last modified March 25 19:41 EDT 2017. Contains 284082 sequences.