Smallest number at distance 3n from nearest prime.

[Dean Hickerson]

Jonathan Post wrote:

> Smallest number at distance 3n from nearest prime.
> 
> 2, 0, 119, 896, 1339, 1342, ...

The distance from 0 to the nearest prime is 2, not 3.  a(1) should be 26.

> Comment: analogue of A051728 which uses 2n. "Prime" is restricted to
> positive integers. Largest number less than the mean of the smallest
> prime gap of size at least 6n.

The last sentence is incorrect.  E.g. for n=1, the first gap of size at
least 6 is from 23 to 29, and a(1) equals the mean of 23 and 29.

> This is the 3rd row of an array whose first row is A000040, and second
> row is A051728.

For the first row, a(n) would be the smallest number at distance n from
the nearest prime.  That's not A000040.

In A051728, it appears that "nearest prime" means the nearest prime
other than the number itself; otherwise 23 and 53 would have distances
0, not 4 and 6.  But if we're using that definition, then the 119 above
should be 53, which is at distance 6 from 47 and 59.

> Is it interesting to code this, and show the next few
> rows, perhaps by showing the array by antidiagonals?

In my opinion, no.  Whichever definition of "nearest prime" you use, the
n-th row of the table just consists of every n-th term from the first
row, so I don't see why any but the first row should be in the OEIS.

Dean Hickerson
dean at math.ucdavis.edu