A077199 Smallest k such that both k and k+n are squarefree.

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

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