login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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