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%I A248124 #13 Aug 01 2019 03:48:18
%S A248124 1,19,1,20,1,95,1,4,1,242,241,478,1,23,1,5,7,109,1,17,1,227,467,37,1,
%T A248124 209,1,330,2077,17,1073,816,1,27,109,71,1,43,1,41,145,151,1,43,1,59,
%U A248124 71,587,1,87,1775,344,1773,1127,1,49,1
%N A248124 Least integer m > 0 such that gcd(m,n) = 1 and (m+n) | (C(m)+C(n)), where C(k) refers to the k-th Catalan number, binomial(2k,k)/(k+1).
%C A248124 Conjecture: a(n) exists for all n > 3.
%H A248124 Zhi-Wei Sun, <a href="/A248124/b248124.txt">Table of n, a(n) for n = 4..10000</a>
%e A248124 a(5) = 19 since 5 is relatively prime to 19 and 5 + 19 = 24 divides C(5) + C(19) = 42 + 1767263190 = 1767263232 = 24*73635968.
%t A248124 Do[m=1;Label[aa];If[GCD[m,n]==1&&Mod[CatalanNumber[m]+CatalanNumber[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,4,60}]
%Y A248124 Cf. A000108, A247824, A247937, A247940, A248123, A248125.
%K A248124 nonn
%O A248124 4,2
%A A248124 _Zhi-Wei Sun_, Oct 01 2014

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