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A264840 Consider the sequence {3k, k >= 1}, and write down the numbers of consecutive terms that are squarefree. 2

%I

%S 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,

%T 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,

%U 2,2,1,1,2,2,1,1,2,1,1,1,2,1,1,2,2,1,1

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

%C 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).

%H Peter J. C. Moses, <a href="/A264840/b264840.txt">Table of n, a(n) for n = 1..1000</a>

%e 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, ....

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

%Y Cf. A005117, A261034, A264843.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Nov 26 2015

%E More terms from _Peter J. C. Moses_, Nov 26 2015

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Last modified October 21 18:36 EDT 2021. Contains 348155 sequences. (Running on oeis4.)