

A077199


Smallest k such that both k and k+n are squarefree.


0



2, 3, 2, 2, 2, 5, 3, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 7, 3, 2, 5, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 5, 3, 2, 2, 5, 6, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 5, 3, 2, 2, 2, 3, 2, 2, 2, 3
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OFFSET

1,1


COMMENTS

If a(n) = 3 or 7 then a(n+1) = 2 or 6 respectively.
Conjecture: every term is < 10, i.e. for every n at least one of the numbers n+2, n+3, n+5, n+6 or n+7 is squarefree.
The conjecture is false. Here are 9 counterexamples, each of which is less than 10000: 1857, 2522, 3570, 4470, 6169, 6645, 7981, 9553, 9745. There are 16 counterexamples within the first 10000 squarefree numbers.  Harvey P. Dale, May 24 2014


LINKS

Table of n, a(n) for n=1..70.


EXAMPLE

a(12) = 2 as 2+12 = 14 is squarefree.


MATHEMATICA

With[{sqfree=Select[Range[2, 20], SquareFreeQ]}, Flatten[ Table[ Select[ sqfree+ n, SquareFreeQ, 1]n, {n, 70}]]] (* Harvey P. Dale, May 21 2014 *)


PROG

(PARI) a(n) = {k = 2; while(!issquarefree(k)  !issquarefree(k+n), k++); k; } \\ Michel Marcus, May 24 2014


CROSSREFS

Sequence in context: A187757 A286529 A306225 * A145390 A270026 A340703
Adjacent sequences: A077196 A077197 A077198 * A077200 A077201 A077202


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Nov 01 2002


EXTENSIONS

Corrected and extended by Harvey P. Dale, May 21 2014


STATUS

approved



