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A076259 Gaps between squarefree numbers: A005117(n+1) - A005117(n). 8
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

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

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. A020753, A020754, A076260.

Sequence in context: A036036 A228531 A244316 * A260533 A107359 A112377

Adjacent sequences:  A076256 A076257 A076258 * A076260 A076261 A076262

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 03 2002

STATUS

approved

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Last modified June 23 21:29 EDT 2017. Contains 288675 sequences.