A218049 Smallest k such that the n numbers k^2 + 1, (k+1)^2 + 1, ..., (k+n-1)^2 + 1 are divisible by a square.

7, 117, 5742, 455356, 35952791

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Example

a(3) = 5742 as 5742^2+1, 5743^2+1 and 5744^2+1 are divisible by squares.
5742^2+1 = 5 * 17 ^ 2 * 22817;
5743^2+1 = 2 * 5 ^ 2 * 701 x 941;
5744^2+1 = 109 ^ 2 * 2777.

Mathematica

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

Crossrefs

Cf. A002522, A217798, A218048.

Sequence in context: A297308 A077394 A009696 * A097202 A163202 A213112

Adjacent sequences: A218046 A218047 A218048 * A218050 A218051 A218052

Keyword

nonn,hard

Author

Michel Lagneau, Oct 19 2012

Extensions

a(5) from Giovanni Resta, Oct 21 2012

Status

approved