Open Problem Garden

On January 18th, 2012 Anonymous says:

In the initial comment five values are stated to be not divisible by 3, 5, 7, and 11. That is true for 1 and 3160 but not for 2, 10, and 3159:

The last base-3-digit of 2 is 2. The last base-11-digit of 10 is 10. The last base-5-digit 3159 is 4.

Or check these facts:

${{2 \times 2} \choose 2} = 6 = 3 \times 2$

${{2 \times 10} \choose 10} = 184756 = 11 \times 16796$

2 and 3159 are not in the sequence A030979 (mentioned in the bibliography).

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