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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 (list; graph; refs; listen; history; text; internal format)
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. 235-253.

E. Fogels, On the average values of arithmetic functions, Proc. Cambridge Philos. Soc. 1941, 37: 358-372.

L. Marmet, First occurrences of squarefree gaps...

L. Marmet, First occurrences of square-free 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) 26:263-268.

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

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Last modified December 11 21:00 EST 2019. Contains 329937 sequences. (Running on oeis4.)