OFFSET
1,2
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.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
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).
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 02 2014
STATUS
approved