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A020754 Increasing gaps between squarefree numbers (lower end). 12
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)
OFFSET

1,2

COMMENTS

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

LINKS

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

Tsz Ho Chan, New small gaps between squarefree numbers, arXiv:2110.09990 [math.NT]

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.

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.

PROG

(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

(PARI) r=0; L=1; forsquarefree(n=2, 10^8, t=n[1]-L; if(t>r, r=t; print1(L", ")); L=n[1]) \\ Charles R Greathouse IV, Oct 22 2021

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

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Last modified October 25 05:57 EDT 2021. Contains 348239 sequences. (Running on oeis4.)