A264840 Consider the sequence {3k, k >= 1}, and write down the numbers of consecutive terms that are squarefree.

2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1

Offset

1,1

Comments

This is a (1,2)-sequence (every term is either 1 or 2), since out of every three consecutive multiples of 3 at least one is not squarefree (it is divisible by 9).

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Example

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, .... The squarefree ones are (3,6), (15), (21), (30,33), .... So a(1)=2, a(2)=1, a(3)=1, a(4)=2, ....

Mathematica

Map[Count[#, True]&, DeleteCases[Split[Map[SquareFreeQ[3#]&, Range[400]]], {___, False, ___}]] (* Peter J. C. Moses, Nov 26 2015 *)

Crossrefs

Cf. A005117, A261034, A264843.

Sequence in context: A276711 A351451 A191322 * A308188 A046219 A088978

Adjacent sequences: A264837 A264838 A264839 * A264841 A264842 A264843

Keyword

nonn

Author

Vladimir Shevelev, Nov 26 2015

Extensions

More terms from Peter J. C. Moses, Nov 26 2015

Status

approved