

A020754


Increasing gaps between squarefree numbers (lower end).


11



1, 3, 7, 47, 241, 843, 22019, 217069, 1092746, 8870023, 221167421, 47255689914, 82462576219, 1043460553363, 79180770078547, 3215226335143217, 23742453640900971, 125781000834058567
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..18.
Michael J. Mossinghoff, Tomás Oliveira e Silva, and Tim Trudgian, The distribution of kfree numbers, arXiv:1912.04972 [math.NT], 2019. See Table 3, p. 14.


FORMULA

a(n) = A020755(n)  A020753(n); also a(n) = A020754(n+[n>10])  1 at least for n < 19.  M. F. Hasler, Dec 28 2015


EXAMPLE

The first gap in A005117 occurs between 1 and 2 and has length 1. The next largest gap occurs between 3 and 5 and has length 2. The next largest gap is between 7 and 10 and has length 3. Etc. We are only interested in gaps that set new records.


PROG

(PARI) A020754(n)=for(k=L=1, 9e9, issquarefree(k)next; kL>=n&&return(L); L=k) \\ For illustrative purpose only, not useful for n>10.  M. F. Hasler, Dec 28 2015


CROSSREFS

Cf. A005117, A020753, A020755, A045882, A051681.
Sequence in context: A064457 A318087 A005650 * A052381 A219877 A031440
Adjacent sequences: A020751 A020752 A020753 * A020755 A020756 A020757


KEYWORD

nonn,hard,nice,changed


AUTHOR

David W. Wilson


EXTENSIONS

Thanks to Christian G. Bower for additional comments.
a(16)a(18) from A045882 by Jens Kruse Andersen, May 01 2015


STATUS

approved



