[seqfan] Re: Typo in B-file for A063539
Neil Sloane
njasloane at gmail.com
Thu Apr 2 18:52:05 CEST 2020
Allan, you said
> A(7910) ought to be 29925 (the example I gave above), but is instead given
as 9925,
Actually the b-file says A(7910) = 9795, and A(7943) = 9925. I think that
illustrates how errors creep in!!
I am recomputing the b-file.
Thanks for the heads-up
Best regards
Neil
Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
On Thu, Apr 2, 2020 at 12:37 PM Allan Wechsler <acwacw at gmail.com> wrote:
> A063539 collects numbers whose largest prime factor is less than the square
> root. For example, 29925 = 3^2 * 5^2 * 7 * 19, and 19^2 is only 361, much
> smaller than 29925.
>
> An interesting feature of this sequence is that it has constant asymptotic
> density; HAKMEM item 29 (Schroeppel) identifies the density as (1 - ln 2),
> without proof.
>
> Because of this intriguing feature, it's interesting to look at the graph
> (which of course looks like a straight line), and this reveals an odd blot
> under the line, which I have traced to a typo in the B-file.
>
> A(7910) ought to be 29925 (the example I gave above), but is instead given
> as 9925, which should not be in the sequence because its largest prime
> factor is 397.
>
> I wonder how typos like this can creep in -- the text of the B-file ought
> to be copied directly from program output, and never pass through human
> editorial hands which might drop a digit, as seems to have happened here.
>
> (Also, the comments should include the slope of the line, ideally with a
> citation to someplace that proves the identity.)
>
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