A225743 Triangular array: row n is least squarefree word of length n using positive integers.

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

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 *)
Map[IntegerExponent[2*#, 2] &, Range[Range[33]]] (* A225743 array, by formula *)
(* Peter J. C. Moses, Sep 03 2013 *)

Crossrefs

Cf. A001511 (the limiting sequence)

Sequence in context: A271608 A087740 A029439 * A218828 A075117 A279387

Adjacent sequences: A225740 A225741 A225742 * A225744 A225745 A225746

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Sep 03 2013

Status

approved