A248137 Least positive integer m such that m + n divides M(m) + M(n), where M(.) is given by A001006.

1, 1, 244, 1, 23, 4, 1, 1, 3494, 1, 68058, 4, 20, 18, 35, 1, 4, 14, 32, 13, 21, 1, 5, 22, 172, 7, 8, 1, 1, 28, 14, 19, 2, 178, 15, 227, 2, 6, 109, 1, 22, 122, 47, 22, 126, 1, 43, 60, 41, 18, 24, 1, 13, 23, 21, 24, 126, 1, 152, 6

Offset: 1

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0.

Examples

			a(5) = 23 since 5 + 23 = 28 divides M(5) + M(23) = 21 + 1129760415 = 1129760436 = 28*40348587.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..2187

Crossrefs

Cf. A001006, A247824, A247937, A247940, A248124, A248125, A248133, A248136, A248139, A248142.

Programs

Mathematica

M[n_]:=Sum[Binomial[n,2k]Binomial[2k,k]/(k+1),{k,0,n/2}]
Do[m=1;Label[aa];If[Mod[M[m]+M[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]