[seqfan] Re: Typo in B-file for A063539
jean-paul.allouche at imj-prg.fr
Fri Apr 10 22:17:00 CEST 2020
I am not sure that my message below came through.
Actually there is something more: the density being
(1 - ln 2), this implies that the n-th term of the sequence
is equivalent to Cn with C = 1/(1-ln (2)) which is about 3.259
(so that it is not 3.7642*n as indicated in the Formula Section.
Since I have a bad internet connection, it would be good if
someone could have a quick check and make the corresponding
changes in A063539.
Many thanks in advance
Le 03/04/2020 à 18:29, jean-paul allouche a écrit :
> I asked Gérald Tenenbaum about the result stated by Schroeppel.
> He told me that this is, e.g., Exercise 28 (with proof) in his book
> with Jie Wu:
> # GÉRALD TENENBAUM
> <https://www.belin-education.com/gerald-tenenbaum>, JIE WU
> Théorie analytique et probabiliste des nombres
> 307 exercices corrigés
> I double-checked: this is indeed Exercise 28 on Page 26, the solution
> can be found on Page 34. Everything is in French but this should not be
> a problem. Note that the first few pages of the book (including the two
> pages above) are freely accessible on the site of the publisher:
> by clicking on the cover page.
> best wishes
> Le 02/04/2020 à 18:34, Allan Wechsler a écrit :
>> A063539 collects numbers whose largest prime factor is less than the
>> root. For example, 29925 = 3^2 * 5^2 * 7 * 19, and 19^2 is only 361,
>> smaller than 29925.
>> An interesting feature of this sequence is that it has constant
>> 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
>> (which of course looks like a straight line), and this reveals an odd
>> 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
>> 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
>> to be copied directly from program output, and never pass through human
>> editorial hands which might drop a digit, as seems to have happened
>> (Also, the comments should include the slope of the line, ideally with a
>> citation to someplace that proves the identity.)
>> Seqfan Mailing list - http://list.seqfan.eu/
> Seqfan Mailing list - http://list.seqfan.eu/
More information about the SeqFan