A290332 a(n) is the smallest j which satisfies (j^2 + k)/(j + k^2) = n where j,k are integers and j >= k > 0.

1, 5, 5, 10, 27, 69, 12, 38, 20, 103, 14, 335, 19, 1859, 147, 37, 293, 44, 54, 1043, 89, 50, 38, 404, 36, 33, 367, 263, 45, 77, 84, 147, 12350, 129, 57, 1962, 49, 37665, 109, 217, 42185, 5225, 103, 1110, 119, 101, 65, 1770, 550, 2507, 88, 1180, 153, 9683509, 171, 122, 407, 214

Offset: 1

Author

Zhining Yang, Jul 27 2017

Keywords

• nonn

Examples

			a(13) = 19 since 13 = (19^2 + 3)/(19 + 3^2) and there is no integer j < 19 such that 13 = (j^2 + k)/(j + k^2) with j > k > 1.
		

Links

• Zhining Yang, Table of n, a(n) for n = 1..300
• Zhining Yang, Blog

Crossrefs

Cf. A290333.

Programs

Mathematica

Table[SelectFirst[Range[10^4], Function[j, AnyTrue[Range[j], Function[k, (j^2 + k)/(j + k^2) == n]]]], {n, 32}] (* Michael De Vlieger, Aug 16 2017 *)

PARI

for(n=1,100,for(b=1,10^8,t=b*(b*n-1);a=floor((n+sqrt(n*n+4*t))/2);if(a*(a-n)==t,print1(a, ", ");break)))