[seqfan] Re: Biprimes of K

[M. F. Hasler]

On Wed, Sep 17, 2014 at 9:40 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
> I'll explain more:
> _Undelined_ is NOT "eliminated", sorry!
> An integer might be underlined several times.
> We are interested in integer that have never been underlined (once or more).

I understood this (I used "eliminated" as (bad) synonym for "underlined"),
but I think that, since underlined integers are excluded from the set
of "primes",
they should not be used for the sieving process.
(Usually the primes are the "surviving" numbers (except for 1),
but also *exactly* those which were used (as a kind of "pivot") for
the sieving.)
Can you confirm this?

What was a bit confusing in the OP was that you wrote
"we start with the first 2,....(then) we go to the first "3",...
(then) we go to the first "4",...(then) we go to the first "5",..."
This gives the illusion that the numbers are chosen in increasing order,
but unless I misunderstand the intended scheme, you mean
each time: "then we go the the next number not yet underlined ...."
(next = next in the list, not next larger wherever it is?)

In your list, the 5 is followed by 8, so I assume that the next number
to be used after the 5 is the 8, and the 7 is never used.
Can you confirm ?

M.

> Best,
> É.
> ----------------------------------------
> Hello SeqFans,
> what are the "biprimes" of K?
> K = http://oeis.org/A026242
>
> K = 1, 1, 2, 3, 2, 4, 3, 5, 6, 4, 7, 8, 5, 9, 6, 10, 11, 7, 12, 8, 13, 14, 9, 15, 16, 10, 17, 11, 18, 19, 12, 20, 21, 13, 22, 14, 23, 24, 15, 25, 16, 26, 27, 17, 28, 29, 18, 30, 19, 31, 32, 20, 33, 21, 34, 35, 22, 36, 37, 23, 38, 24, 39, 40, 25, 41, ...
>
> Let's start with the first "2" of K
> and underline one on two terms
> (this is 2-3-6-7-5-...)
> We then go back to the first "3"
> and underline one on three terms
> (this is 3-4-5-10-12-...)
> We then go back to the first "4"
> and underline one on four terms
> (this is 4-9-7-14-...)
> We then go back to the first "5"
> and underline one on five terms
> (this is 5-7-9-11-...)
> etc.
> At the end, we will see that some
> terms are not underlined: the
> "biprimes" of K.
>
> BIP = 2,3,4,5,8,15,...
>
> What are the next ones (if there are)?
>
> Best,
> É.
>
>
>
> -----Message d'origine-----
> De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de M. F. Hasler
> Envoyé : mercredi 17 septembre 2014 15:35
> À : Sequence Fanatics Discussion list
> Objet : [seqfan] Re: Biprimes of K
>
> On Wed, Sep 17, 2014 at 3:16 AM, L. Edson Jeffery <lejeffery2 at gmail.com> wrote:
>> Please check your code. Applying the process to 3 should mark
>> (underline) the first occurrence of 20 and applying it to 7 should
>> mark the second occurrence of 20. So 20 is not in the BIP sequence,
>> meaning that your
>
> I don't agree, since the the first 7 is eliminated in the first step and the second 7 is eliminated when the procedure is applied to 4 so it is never used.
> (Also, 7 is not in Eric's list and I think as is the case for Eratothenes' sieve, only the "(bi)primes" of this list are to be used in that way.) Unless I misunderstood the procedure, of course...
>
> Maximilian