A264843 Maximal numbers of consecutive positive integers congruent to 1 modulo 3 that are all squarefree.

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

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 A379880 A029211

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