%I #9 Oct 05 2014 20:55:37

%S 1,1,2,1,3,8,2,6,6,45,9,4,15,2,13,17,4,12,9,8,11,6,101,20,2,15,7,50,4,

%T 183,48,15,9,5,4,4,157,1,123,4,13,112,76,4,7,13,44,2,16,28,83,202,114,

%U 50,85,31,14,62,19,25

%N Least positive integer m such that m + n divides prime(m^2) + prime(n^2).

%C Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1)/2 for all n > 1.

%C See also the comments in A248052.

%H Zhi-Wei Sun, <a href="/A248354/b248354.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 2 since 2 + 3 = 5 divides prime(2^2) + prime(3^2) = 7 + 23 = 30.

%t Do[m = 1; Label[aa]; If[Mod[Prime[m^2] + Prime[n^2], m + n] == 0, Print[n, " ", m]; Goto[bb]]; m = m + 1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

%o (PARI) a(n)=my(N=prime(n^2),m); while((prime(m++^2)+N)%(m+n), ); m \\ _Charles R Greathouse IV_, Oct 05 2014

%Y Cf. A000040, A000290, A011757, A247824, A247975, A248052.

%K nonn

%O 1,3

%A _Zhi-Wei Sun_, Oct 05 2014