A266241 Integers n such that average of first n Catalan numbers (A000108) is an integer.

1, 2, 12, 377, 2504, 342317

Offset

1,2

Comments

Integers n such that A014137(n-1) is divisible by n.

Corresponding average values are 1, 1, 6875, ...

Links

Table of n, a(n) for n=1..6.

Example

1 is a term because C(0) mod 1 = 1 mod 1 = 0.
2 is a term because (C(0) + C(1)) mod 2 = (1 + 1) mod 2 = 0.
12 is a term because (C(0) + C(1) + ... + C(10) + C(11)) mod 12 = (1 + 1 + ... + 16796 + 58786) mod 12 = 0.

Prog

(PARI) a(n) = sum(k=0, n, (2*k)!/(k!)^2/(k+1)) % (n+1);
for(n=0, 1e5, if(a(n)==0, print1(n+1", ")));
(Magma) a:=[1]; catalan:=1; sum:=catalan; for n in [2..350000] do catalan:=(catalan*(4*n-6)) div n; sum+:=catalan; if (sum mod n) eq 0 then a[#a+1]:=n; end if; end for; a; // Jon E. Schoenfield, Dec 25 2015

Crossrefs

Cf. A000108, A014137.

Sequence in context: A158261 A215956 A251182 * A012547 A009706 A012551

Adjacent sequences: A266238 A266239 A266240 * A266242 A266243 A266244

Keyword

nonn,more

Author

Altug Alkan, Dec 25 2015

Extensions

a(6) from Jon E. Schoenfield, Dec 25 2015

Status

approved