A055191 -id:A055191 - cp's OEIS frontend

A055179 n-th distinct number to appear in A055171; also the n-th to appear in A055191.

3, 1, 2, 6, 5, 7, 4, 8, 9, 10, 12, 11, 15, 18, 13, 16, 21, 17, 24, 27, 19, 30, 20, 32, 22, 34, 23, 37, 26, 14, 25, 41, 35, 28, 29, 44, 40, 31, 50, 42, 33, 54, 48, 38, 58, 52, 45, 62, 55, 65, 59, 49, 51, 68, 63, 36, 43, 53, 72, 66, 39, 78, 71

Offset: 1

Clark Kimberling, Apr 27 2000

nonn

Conjecture: this sequence is a permutation of the positive integers.

A055186 Cumulative counting sequence: method A (adjective-before-noun)-pairs with first term 0.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Apr 27 2000

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

			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; ...

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

Cf. A005150. For other versions see A051120, A079668, A079686.
Cf. A055168-A055185 (method B) and A055187-A055191 (method A).
Cf. A217760.

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

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

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

A055178 Number of new numbers in n-th segment of A055177; see example line of A055177.

Original entry on oeis.org

1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3, 3, 5, 3, 3, 3, 2, 3, 3, 6, 3, 2, 4, 5, 3, 5, 3, 2, 3, 5, 4, 5, 3

Offset: 1

Clark Kimberling, Apr 27 2000

nonn

Also, the number of new numbers in n-th segment of A055191.

cp's OEIS Frontend

A055179 n-th distinct number to appear in A055171; also the n-th to appear in A055191.

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A055186 Cumulative counting sequence: method A (adjective-before-noun)-pairs with first term 0.

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A055178 Number of new numbers in n-th segment of A055177; see example line of A055177.

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