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%I #5 Sep 27 2014 18:08:28
%S 5,5,15,5,19,30,17,19,15,13,13,24,35,236,33,34,31,90,29,23,27,25,25,
%T 84,47,80,45,190,43,54,41,35,39,1216,37,72,59,212,57,43,55,66,53,86,
%U 51,76,49,60,71,53,69,55,67,222,65,122,63,112,61,264
%N Least integer m > n such that m + n divides L(m) + L(n), where L(k) refers to the Lucas number A000032(k).
%C Conjecture: Let A be any integer not congruent to 3 modulo 6. Define v(0) = 2, v(1) = A, and v(n+1) = A*v(n) + v(n-1) for n > 0. Then, for any integer n > 0, there are infinitely many positive integers m such that m + n divides v(m) + v(n).
%C This implies that a(n) exists for any n > 0.
%H Zhi-Wei Sun, <a href="/A247940/b247940.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 15 since 15 + 3 = 18 divides L(15) + L(3) = 1364 + 4 = 18*76.
%t Do[m=n+1;Label[aa];If[Mod[LucasL[m]+LucasL[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]
%Y Cf. A000032, A247824, A247937.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Sep 27 2014
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