A020753 Sizes of successive increasing gaps between squarefree numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19

Offset

1,2

Comments

The indices of the records in A076259 are 1, 3, 6, 31, 150, 515, 13391, 131964, 664313, ... - R. J. Mathar, Jun 25 2010

Applying the test to squarefree numbers up to 10 million only produces the first ten terms of the sequence. - Harvey P. Dale, May 04 2011

Conjecture: a(n) ~ log(A020754(n))/2. - Thomas Ordowski, Jul 23 2015

Links

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

Formula

a(n) = A020755(n) - A020754(n). - M. F. Hasler, Dec 28 2015

Example

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

Maple

a := 1 ; for n from 2 do if A076259(n) > a then print(n, A076259(n)) ; a := A076259(n) ; end if; end do: # R. J. Mathar, Jun 25 2010

Mathematica

Union[Differences[Select[Range[10000000], SquareFreeQ]]] (* Harvey P. Dale, May 04 2011 *)

Crossrefs

Cf. A005117, A020754, A020755, A045882, A051681, A076259.

Sequence in context: A247397 A194845 A194056 * A353888 A331162 A337843

Adjacent sequences: A020750 A020751 A020752 * A020754 A020755 A020756

Keyword

nonn,hard,more,nice

Author

David W. Wilson

Extensions

Thanks to Christian G. Bower for additional comments.

More terms computed (using data from A020754) by M. F. Hasler, Dec 28 2015

Status

approved