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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. 2

%I

%S 1,5,5,10,27,69,12,38,20,103,14,335,19,1859,147,37,293,44,54,1043,89,

%T 50,38,404,36,33,367,263,45,77,84,147,12350,129,57,1962,49,37665,109,

%U 217,42185,5225,103,1110,119,101,65,1770,550,2507,88,1180,153,9683509,171,122,407,214

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

%H Zhining Yang, <a href="/A290332/b290332.txt">Table of n, a(n) for n = 1..300</a>

%H Zhining Yang, <a href="http://blog.csdn.net/northwolves/article/details/5124287">Blog</a>

%e 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.

%t 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 *)

%o (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)))

%Y Cf. A290333.

%K nonn

%O 1,2

%A _Zhining Yang_, Jul 27 2017

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Last modified October 22 22:14 EDT 2021. Contains 348180 sequences. (Running on oeis4.)