Smallest number at distance 3n from nearest prime.

[Jonathan Post]

Thank you, Dean. I stand corrected on several points.

The corrected 2nd formula, verbally, becomes:
"Largest number less than OR EQUAL TO the mean of the smallest prime
gap of size at least 6n.

By "n-th row of the table" I mean the k-th row, i.e.
"Smallest number at distance k*n from nearest prime."

It might be a good comment or edit for A051728, as you say: "it
appears that 'nearest prime' means the nearest prime other than the
number itself."  In teaching Astronomy, I recall the confusion among
students as to the meaning of "the nearest star to earth" where some
did and some did not understand the Sun to be included in the
description.

Memo to self = apology to seqfans: don't do Math in unairconditioned
house at peak of serious heat wave (it was 107 F and humid at the time
I emailed this one). Not long after, I shut down PCs to avoid the
expected 9and then occurring) brownouts of power.  Some people lost
electricty for days. More than 10 people in southern california died
in that heat wave which broke today.

On 9/4/07, Dean Hickerson <dean at math.ucdavis.edu> wrote:
> 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
>