A264843 - OEIS

%I #23 Jan 12 2016 00:26:04

%S 1,3,2,3,2,3,3,3,3,3,2,3,3,3,2,2,3,3,3,3,3,1,1,3,3,2,3,3,2,3,2,2,3,3,

%T 3,3,3,3,3,3,3,2,1,1,3,3,2,3,1,1,3,3,3,3,3,2,2,3,3,3,3,3,3,3,3,3,3,3,

%U 2,3,3,3,3,2,1,3,3,3,3,3,2,2,3,2,3,3,3

%N Maximal numbers of consecutive positive integers congruent to 1 modulo 3 that are all squarefree.

%C a(n) takes only values 1,2,3, since from every four numbers == 1 (mod 3), at least one is divisible by 4, hence nonsquarefree.

%H Peter J. C. Moses, <a href="/A264843/b264843.txt">Table of n, a(n) for n = 1..1000</a>

%e From the first integers congruent to 1 (mod 3): 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, ..., the squarefree ones are (1), (7,10,13), (19,22), (31,34,37). So, a(1)=1, a(2)=3, a(3)=2, a(4)=3.

%t Map[Count[#,True]&,DeleteCases[Split[Map[SquareFreeQ[3#-2]&,Range[500]]],{___,False,___}]] (* _Peter J. C. Moses_, Nov 26 2015 *)

%o (PARI) lista(nn) = {nb = 0; for (n=0, nn, if (issquarefree(3*n+1), nb++, if (nb, print1(nb, ", ")); nb = 0););} \\ _Michel Marcus_, Dec 15 2015

%Y Cf. A005117, A264778, A264779, A264840.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Nov 26 2015

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