login
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.
4

%I #23 Dec 31 2019 09:28:08

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

%N 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.

%e a(1)= 8 because 8^2 + 1 = A300168(1) = 65 = 7^2 + 4^2.

%e 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.

%e a(3) = 242 because 242^2 + 1 = 58565 is the smallest number that can be expressed in more than 3 ways:

%e 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.

%Y Cf. A300161, A300165, A300168.

%K nonn,hard,more

%O 1,1

%A _Hugo Pfoertner_, Feb 27 2018

%E a(7) from _Robert Price_, Mar 11 2018

%E a(7) corrected, a(8)-a(9) added by _Ray Chandler_, Dec 23 2019

%E a(10) added by _Ray Chandler_, Dec 31 2019