A248133 Least positive integer m such that m + n divides T(m) + T(n), where T(.) is given by A002426.

1, 3, 1, 1, 7, 2, 2, 2, 1, 1, 7, 4, 37, 145, 35, 1, 25, 16, 5, 16, 1, 1, 18, 19, 3, 11, 41, 1, 7, 2, 48, 415, 1, 2, 15, 7, 13, 34, 97, 1, 27, 18, 56, 22, 1, 1, 5, 26, 22, 36, 18, 1, 117, 52, 376, 11, 1, 1, 23, 26

Offset: 1

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 - n + 1 except for n = 274.

Note that a(274) = 188847 > 2*274^2.

Examples

			a(5) = 7 since 5 + 7 divides T(5) + T(7) = 51 + 393 = 444 = 12*37.
a(2539) = 643425 since 2539 + 643425 = 645964 divides T(2539) + T(643425).
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002426, A247824, A247937, A247940, A248124, A248125, A248136, A248137, A248139, A248142.

Programs

Mathematica

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