[gaps between square-free numbers]

[Christian G.Bower]

"N. J. A. Sloane" <njas at research.att.com> wrote:
> Dear seqfans,
> 
> there's an old sequence of David Wilson's that needs a few more
> terms - any volunteers?
> 

A045882 gives the answer:

ID Number: A045882
Sequence:  4,8,48,242,844,22020,217070,1092747,8870024,221167422,
           221167422,47255689915,82462576220,1043460553364,
           79180770078548,3215226335143218
Name:      Smallest term of first run of (at least) n consecutive integers
which
              are not square-free.
Comments:  Solution for n=10 is same as for n=11.
Links:     More information
           Results
           Squarefree numbers
Example:   E.g. n=5 -> {844=2^2*211; 845=5*13^2; 846=2*3^2*47; 847=7*11^2;
              848=2^4*53}.
See also:  Cf. A013929, A051681, A053806.
Keywords:  nonn,nice,hard
Offset:    1
Author(s): Erich Friedman (erich.friedman at stetson.edu)
Extension: a(9) to a(11) from Patrick De Geest (Patrick.DeGeest at ping.be),
              11/98, 01/99. a(12) to a(15) from Louis Marmet (louis at marmet.ca)
and
              David Bernier (ezcos at yahoo.com), 11/1999.
           a(16) was obtained as a result of a team effort by Z.
McGregor-Dorsey et
              al. [Louis Marmet (louis at marmet.ca), Jul 27 2000]

Giving:

> 
> %I A020753
%S A020753 1,2,3,4,5,6,7,8,9,10,12,13,14,15,16
> %N A020753 Sizes of successive increasing gaps between square-free numbers.
%K A020753 nonn,hard
> %O A020753 1,2
> %A A020753 dww
%Y A020753 Cf. A005117, A020754, A020755, A045882, A051681.
> 
> The two related sequences are
> 
> %I A020754
> %S A020754 1,3,7,47,241,843,22019,217069,1092746,8870023,221167421
%T A020754 47255689914,82462576219,1043460553363,79180770078547
> %N A020754 Increasing gaps between square-free numbers (lower end).
%K A020754 nonn,hard
> %O A020754 1,2
> %A A020754 dww
%Y A020754 Cf. A005117, A020753, A020755, A045882, A051681.
> 
> 
> %I A020755
> %S A020755 2,5,10,51,246,849,22026,217077,1092755,8870033,221167433
%T A020755 47255689927,82462576233,1043460553378,79180770078563
> %N A020755 Increasing gaps between square-free numbers (upper end).
%K A020755 nonn,hard
> %O A020755 1,1
> %A A020755 dww
%Y A020755 Cf. A005117, A020754, A020753, A045882, A051681.
> 
> NJAS


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