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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 2 20:05 EDT 2021. Contains 346428 sequences. (Running on oeis4.)