

A020755


Increasing gaps between squarefree numbers (upper end).


5



2, 5, 10, 51, 246, 849, 22026, 217077, 1092755, 8870033, 221167433, 47255689927, 82462576233, 1043460553378, 79180770078563, 3215226335143234, 23742453640900989, 125781000834058586
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OFFSET

1,1


COMMENTS

Up to n=10, a(n) is the upper end of the first gap of length n. However, for n=11 through n=16, a(n) is the upper end of the first gap of length n+1. See A020753.  M. F. Hasler, Dec 28 2015


LINKS

Table of n, a(n) for n=1..18.


FORMULA

a(n) = A020754(n) + A020753(n).  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) A020755(n)=for(k=L=1, 9e9, issquarefree(k)next; kL>=n&&return(k); L=k) \\ M. F. Hasler, Dec 28 2015


CROSSREFS

Cf. A005117, A020754, A020753, A045882, A051681.
Sequence in context: A082593 A124664 A076776 * A018503 A018535 A140304
Adjacent sequences: A020752 A020753 A020754 * A020756 A020757 A020758


KEYWORD

nonn,hard


AUTHOR

David W. Wilson


EXTENSIONS

Thanks to Christian Bower for additional comments.
More terms (computed using data from A020754) added by M. F. Hasler, Dec 28 2015


STATUS

approved



