

A264843


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


2



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, 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, 2, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 2, 2, 3, 2, 3, 3, 3
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OFFSET

1,2


COMMENTS

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.


LINKS

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


EXAMPLE

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.


MATHEMATICA

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


PROG

(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


CROSSREFS

Cf. A005117, A264778, A264779, A264840.
Sequence in context: A168330 A176059 A262785 * A316290 A029211 A246925
Adjacent sequences: A264840 A264841 A264842 * A264844 A264845 A264846


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Nov 26 2015


EXTENSIONS

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


STATUS

approved



