A120623 Numbers n such that the n-th Catalan number C(2n, n)/(n + 1) is divisible by n/3 but not divisible by n.

3, 12, 18, 84, 99, 120, 198, 216, 273, 342, 432, 522, 540, 792, 828, 945, 975, 984, 990, 1035, 1071, 1323, 1377, 1512, 1548, 1575, 1710, 1755, 1863, 2052, 2106, 2226, 2385, 2442, 2790, 2928, 3009, 3015, 3132, 3198, 3483, 3672, 3807, 3915, 3996, 4212, 4428

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(n(n + 1)/3)] && !IntegerQ[ Binomial[2n, n]/n]; Select[ Range@4463, fQ@# &]

Prog

(Python)
A120623_list, b = [], 1
for n in range(1, 10**5):
    if b % n and not (3*b) % n:
        A120623_list.append(n)
    b = b*(4*n+2)//(n+2) # Chai Wah Wu, Mar 30 2016

Crossrefs

Cf. A000108, A014847, A120622.

Sequence in context: A342785 A166038 A052637 * A158517 A043877 A217697

Adjacent sequences: A120620 A120621 A120622 * A120624 A120625 A120626

Keyword

nonn

Author

Robert G. Wilson v, Jun 19 2006

Extensions

Better description from Joel B. Lewis, Nov 15 2006

Status

approved