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).

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, 209, 1, 330, 2077, 17, 1073, 816, 1, 27, 109, 71, 1, 43, 1, 41, 145, 151, 1, 43, 1, 59, 71, 587, 1, 87, 1775, 344, 1773, 1127, 1, 49, 1

Offset: 4

Author

Zhi-Wei Sun, Oct 01 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for all n > 3.

Examples

			a(5) = 19 since 5 is relatively prime to 19 and 5 + 19 = 24 divides C(5) + C(19) = 42 + 1767263190 = 1767263232 = 24*73635968.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 4..10000

Crossrefs

Cf. A000108, A247824, A247937, A247940, A248123, A248125.

Programs

Mathematica

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}]