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a(n) = 1 + (binomial(2n,n) mod n).
3

%I #11 Jan 05 2017 02:55:28

%S 1,1,3,3,3,1,3,7,3,7,3,5,3,7,1,7,3,7,3,1,7,7,3,13,3,7,21,1,3,5,3,7,10,

%T 7,8,17,3,7,21,21,3,1,3,5,1,7,3,13,3,7,4,45,3,7,33,33,40,7,3,37,3,7,

%U 13,7,6,1,3,37,67,41,3,37,3,7,46,33,1,67,3,21,21,7,3

%N a(n) = 1 + (binomial(2n,n) mod n).

%H Harry J. Smith, <a href="/A059289/b059289.txt">Table of n, a(n) for n = 1..5000</a>

%p [seq((binomial(2*n,n) mod (n))+1,n=1..50)];

%t 1 + Table[Mod[Binomial[2*n, n], n], {n,1,25}] (* _G. C. Greubel_, Jan 04 2017 *)

%o (PARI) { for (n = 1, 5000, write("b059289.txt", n, " ", 1 + binomial(2*n, n) % n); ) } \\ _Harry J. Smith_, Jun 25 2009

%Y Cf. A053214, A059288.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jan 25 2001