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Revision History for A225743

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A225743

Triangular array: row n is least squarefree word of length n using positive integers.
(history; published version)

#18 by N. J. A. Sloane at Sun Dec 04 19:46:31 EST 2016

MATHEMATICA

(* _Peter J. C. Moses, _, Sep 03 2013 *)

Discussion

Sun Dec 04

19:46

OEIS Server: https://oeis.org/edit/global/2576

#17 by N. J. A. Sloane at Mon Sep 09 03:29:52 EDT 2013

STATUS

reviewed

approved

#16 by Charles R Greathouse IV at Thu Sep 05 14:04:20 EDT 2013

STATUS

proposed

reviewed

Discussion

Thu Sep 05

14:06

Clark Kimberling: Please recycle A225743.

#15 by Clark Kimberling at Thu Sep 05 08:54:22 EDT 2013

STATUS

editing

proposed

Discussion

Thu Sep 05

14:04

Charles R Greathouse IV: I reject the argument with A002260 -- not only is that more basic, but "other stuff exists" is insufficient in general. But I think this sequence is okay -- it has enough justification to stand on its own. Still, with deference to Ralf, I'll wait for a third editor to look this over.

#14 by Ralf Stephan at Thu Sep 05 03:00:33 EDT 2013

STATUS

proposed

editing

Discussion

Thu Sep 05

08:54

Clark Kimberling: A001511 doesn't mention the distinctive property that each row of A225743 has - it's is basically a property of those rows, not of A001511.  It seems to me that rejecting A225743 would be like rejecting A002260 because of its relation to A000027.

#13 by Clark Kimberling at Tue Sep 03 16:08:52 EDT 2013

STATUS

editing

proposed

Discussion

Thu Sep 05

03:00

Ralf Stephan: Clark, what does this add to A001511? As it is now, I propose to reject this triangle.

#12 by Clark Kimberling at Tue Sep 03 16:08:42 EDT 2013

EXAMPLE

1

1 2

1 2 1

1 2 1 3

1 2 1 3 1

1 2 1 3 1 2

1 2 1 3 1 2 1

1 2 1 3 1 2 1 4

1 2 1 3 1 2 1 4 1

1 2 1 3 1 2 1 4 1 2

MATHEMATICA

Map[IntegerExponent[2*#, 2] &, Range[Range[33]]] (* A225743 array, by formula *)

#11 by Clark Kimberling at Tue Sep 03 15:02:48 EDT 2013

NAME

allocated for Clark KimberlingTriangular array: row n is least squarefree word of length n using positive integers.

DATA

1, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 4

OFFSET

1,3

COMMENTS

Squarefree means that the word contains no consecutive identical subwords.

LINKS

Clark Kimberling, <a href="/A225743/b225743.txt">Table of n, a(n) for n = 1..10000</a>

EXAMPLE

The first 10 rows are shown here:

1

1 2

1 2 1

1 2 1 3

1 2 1 3 1

1 2 1 3 1 2

1 2 1 3 1 2 1

1 2 1 3 1 2 1 4

1 2 1 3 1 2 1 4 1

1 2 1 3 1 2 1 4 1 2

1 contains no square; 11 contains a square but 12 does not; 121 contains no square; both 1211 and 1212 have squares but 1213 does not.

MATHEMATICA

squareFreeQ[string_] := StringFreeQ[string, a__ ~~ a__]; t = {}; s = Table[AppendTo[t, NestWhile[# + 1 &, 1, ! squareFreeQ[ToString[FromDigits[Append[t, #]]]] &]], {20}];

TableForm[s] (* A225743 array *)

Flatten[s] (* A225743 sequence *)

(* Peter Moses, Sep 03 2013 *)

CROSSREFS

Cf. A001511 (the limiting sequence)

KEYWORD

allocated

nonn,tabl,easy

AUTHOR

Clark Kimberling, Sep 03 2013

STATUS

approved

editing

#10 by Clark Kimberling at Tue Sep 03 14:38:37 EDT 2013

NAME

allocated for Clark Kimberling

KEYWORD

recycled

allocated

#9 by Joerg Arndt at Tue Sep 03 12:27:36 EDT 2013

STATUS

editing

approved