

A053797


Lengths of successive gaps between squarefree numbers.


8



1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 3, 1, 2, 2, 2, 1
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OFFSET

1,2


LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000
M. Filaseta and O. Trifonov, On Gaps between Squarefree Numbers. In Analytic Number Theory, Vol 85, 1990, Birkhauser, Basel, pp. 235253.
E. Fogels, On the average values of arithmetic functions, Proc. Cambridge Philos. Soc. 1941, 37: 358372.
L. Marmet, First occurrences of squarefree gaps...
L. Marmet, First occurrences of squarefree gaps and an algorithm for their computation, arXiv preprint arXiv:1210.3829 [math.NT], 2012.  From N. J. A. Sloane, Jan 01 2013
K. F. Roth, On the gaps between squarefree numbers, J. London Math. Soc. 1951 (2) 26:263268.


EXAMPLE

The first gap is at 4 and has length 1; the next starts at 8 and has length 2 (since neither 8 nor 9 are squarefree).


MAPLE

SF:= select(numtheory:issqrfree, [$1..1000]):
map(``, select(`>`, SF[2..1]SF[1..2], 1), 1); # Robert Israel, Sep 22 2015


MATHEMATICA

ReplaceAll[Differences[Select[Range@384, SquareFreeQ]]  1, 0 > Nothing] (* Michael De Vlieger, Sep 22 2015 *)


CROSSREFS

Gaps between terms of A005117.
Cf. A005117, A053806.
Sequence in context: A001179 A001876 A033182 * A254011 A002635 A275806
Adjacent sequences: A053794 A053795 A053796 * A053798 A053799 A053800


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Apr 07 2000


EXTENSIONS

Offset set to 1 by Peter Kagey, Sep 29 2015


STATUS

approved



