OFFSET
1,2
COMMENTS
From Gus Wiseman, Jun 11 2024: (Start)
Also the length of the n-th maximal run of nonsquarefree numbers. These runs begin:
4
8 9
12
16
18
20
24 25
27 28
32
36
40
44 45
48 49 50
(End)
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, Birkhäuser, 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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 07 2000
EXTENSIONS
Offset set to 1 by Peter Kagey, Sep 29 2015
STATUS
approved