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A020754
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Increasing gaps between squarefree numbers (lower end).
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12
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1, 3, 7, 47, 241, 843, 22019, 217069, 1092746, 8870023, 221167421, 47255689914, 82462576219, 1043460553363, 79180770078547, 3215226335143217, 23742453640900971, 125781000834058567
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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We only consider gaps that set new records. The first gap of size 12 occurs (at 221167421) before the first gap of size 11 (at 262315466) and so for n>10, the n-th term in this sequence does not correspond to the first gap of length n. See A020753. - Nathan McNew, Dec 02 2020
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LINKS
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Table of n, a(n) for n=1..18.
Michael J. Mossinghoff, Tomás Oliveira e Silva, and Tim Trudgian, The distribution of k-free numbers, arXiv:1912.04972 [math.NT], 2019. See Table 3, p. 14.
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FORMULA
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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
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EXAMPLE
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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.
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PROG
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(PARI) A020754(n)=for(k=L=1, 9e9, issquarefree(k)||next; k-L>=n&&return(L); L=k) \\ For illustrative purpose only, not useful for n>10. - M. F. Hasler, Dec 28 2015
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CROSSREFS
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Cf. A005117, A020753, A020755, A045882, A051681.
Sequence in context: A064457 A318087 A005650 * A052381 A219877 A031440
Adjacent sequences: A020751 A020752 A020753 * A020755 A020756 A020757
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KEYWORD
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nonn,hard,nice
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AUTHOR
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David W. Wilson
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EXTENSIONS
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Thanks to Christian G. Bower for additional comments.
a(16)-a(18) from A045882 by Jens Kruse Andersen, May 01 2015
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STATUS
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approved
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