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 A076259 Gaps between squarefree numbers: a(n) = A005117(n+1) - A005117(n). 10
 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 4, 2, 2, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 3, 1, 4, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 1, 3, 2, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This sequence is unbounded, as a simple consequence of the Chinese remainder theorem. - Thomas Ordowski, Jul 22 2015 Conjecture: lim sup_{n->oo} a(n)/log(A005117(n)) = 1/2. - Thomas Ordowski, Jul 23 2015 a(n) = 1 infinitely often since the density of the squarefree numbers, 6/Pi^2, is greater than 1/2. In particular, at least 2 - Pi^2/6 = 35.5...% of the terms are 1. - Charles R Greathouse IV, Jul 23 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = Pi^2/6 (A013661). - Amiram Eldar, Oct 21 2020 EXAMPLE As 24 = 3*2^3 and 25 = 5^2, the next squarefree number greater A005117(16) = 23 is A005117(17) = 26, therefore a(16) = 26-23 = 3. MAPLE A076259 := proc(n) A005117(n+1)-A005117(n) ; end proc: # R. J. Mathar, Jan 09 2013 MATHEMATICA Select[Range[200], SquareFreeQ] // Differences (* Jean-François Alcover, Mar 10 2019 *) PROG (Haskell) a076259 n = a076259_list !! (n-1) a076259_list = zipWith (-) (tail a005117_list) a005117_list -- Reinhard Zumkeller, Aug 03 2012 (PARI) t=1; for(n=2, 1e3, if(issquarefree(n), print1(n-t", "); t=n)) \\ Charles R Greathouse IV, Jul 23 2015 CROSSREFS Cf. A005117, A013661, A020753, A020754, A076260. Sequence in context: A334302 A228531 A244316 * A260533 A107359 A307641 Adjacent sequences:  A076256 A076257 A076258 * A076260 A076261 A076262 KEYWORD nonn,easy,changed AUTHOR Reinhard Zumkeller, Oct 03 2002 STATUS approved

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Last modified October 25 06:05 EDT 2020. Contains 338011 sequences. (Running on oeis4.)