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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. 0
7, 117, 5742, 455356, 35952791 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 20 10:25 EDT 2022. Contains 353871 sequences. (Running on oeis4.)