OFFSET
1,2
COMMENTS
Conjecture: a(n) exists for all n > 0. Moreover, for n > 66 we have a(n) < n except for n = 364, 408.
a(n) = n for n = 1, 2, 6, 15, 20, 28, 66, ... The next term, if it exists, is greater than 10^4. - Derek Orr, Oct 01 2014
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 5 since 3 + 5 = 8 divides C(6,3) + C(10,5) = 20 + 252 = 272.
MATHEMATICA
Do[m=1; Label[aa]; If[Mod[Binomial[2m, m]+Binomial[2n, n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
PROG
(PARI)
a(n)=m=1; while((binomial(2*m, m)+binomial(2*n, n))%(m+n), m++); m
vector(100, n, a(n)) \\ Derek Orr, Oct 01 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 01 2014
STATUS
approved