A300167 Numbers n such that n^2+1 can be expressed as j^2+k^2, j>k>1, gcd(j,k)=1, in more ways than for any smaller n.

8, 47, 242, 2163, 21042, 72662, 1555572, 16485763, 169053487, 2017326722

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Example

a(1)= 8 because 8^2 + 1 = A300168(1) = 65 = 7^2 + 4^2.
a(2) = 47 because it is the smallest n leading to more than 1 way of expressing n^2+1 : 47^2 + 1 = 2010 = 43^2 + 19^2 = 41^2 + 23^2 = 37^2 + 29^2.
a(3) = 242 because 242^2 + 1 = 58565 is the smallest number that can be expressed in more than 3 ways:
  58565 = 241^2 + 22^2 = 239^2 + 38^2 = 223^2 + 94^2 = 214^2 + 113^2 = 209^2 + 122^2 = 206^2 + 127^2 = 193^2 + 146^2.

Crossrefs

Cf. A300161, A300165, A300168.

Sequence in context: A081279 A099110 A106393 * A029760 A139262 A026900

Adjacent sequences: A300164 A300165 A300166 * A300168 A300169 A300170

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Feb 27 2018

Extensions

a(7) from Robert Price, Mar 11 2018

a(7) corrected, a(8)-a(9) added by Ray Chandler, Dec 23 2019

a(10) added by Ray Chandler, Dec 31 2019

Status

approved