A218049 - OEIS

%I #14 Oct 21 2012 07:51:39

%S 7,117,5742,455356,35952791

%N Smallest k such that the n numbers k^2 + 1, (k+1)^2 + 1, ..., (k+n-1)^2 + 1 are divisible by a square.

%e a(3) = 5742 as 5742^2+1, 5743^2+1 and 5744^2+1 are divisible by squares.

%e 5742^2+1 = 5 * 17 ^ 2 * 22817;

%e 5743^2+1 = 2 * 5 ^ 2 * 701 x 941;

%e 5744^2+1 = 109 ^ 2 * 2777.

%t cnt = 0; k = 0; Table[While[cnt < n, k++; If[! SquareFreeQ[k^2+1], cnt++, cnt = 0]]; k - n + 1, {n, 4}]

%Y Cf. A002522, A217798, A218048.

%K nonn,hard

%O 1,1

%A _Michel Lagneau_, Oct 19 2012

%E a(5) from _Giovanni Resta_, Oct 21 2012