A257115 - OEIS

%I #25 Apr 28 2015 14:12:46

%S 1,3,15,15,49,483,5049,6347,144945

%N Smallest k such that none of k + 1, k + 3,... k + 2n - 1 are squarefree and all of k + 2, k + 4,... k + 2n are squarefree.

%C For any x, one of x+2, x+4, ..., x+18 is divisible by 9 and thus not squarefree, so a(n) does not exist for n >= 9. - _Robert Israel_, Apr 27 2015

%e a(0) = 1 because 1 + 0 = 1 is squarefree.

%e a(1) = 3 because 3 + 1 = 4 is not squarefree and 3 + 2 = 5 is squarefree.

%o (PARI) a(n)=k=1;while(k,c=0;for(i=1,n,if(!issquarefree(k+2*i-1)&&issquarefree(k+2*i),c++);if(issquarefree(k+2*i-1)||!issquarefree(k+2*i),c=0;break));if(c==n,return(k));k++)

%o vector(9,n,n--;a(n)) \\ _Derek Orr_, Apr 27 2015

%Y Cf. A257108, A257116.

%K nonn,fini,full

%O 0,2

%A _Juri-Stepan Gerasimov_, Apr 25 2015

%E Corrected and extended by _Derek Orr_, Apr 27 2015