[seqfan] Re: Biprimes of K

[M. F. Hasler]

PS: I implemented the other sieve (which also ("re")uses underlined numbers)
and applied it to A026242(1..10^4) :

{A=vector(10^4); for(j=1, #A, A[min(A000201(j), #A)]=j;
A[min(A001950(j), #A)]=j); A026242=A[1..#A-1]}
do2=(k,A=A026242)->forstep(i=k+A[k],#A,A[k],K[i]=0)
for(k=3,#K=A026242,do2(k))
select(f->f,K)
% = [1, 1, 2, 3, 4, 5, 8, 15, 50]

Thus, if underlined numbers are also used to sieve, then if I start
with as many as 10^4 terms, 50 is the largest non-underlined term, so
it is probably the last term even if the infinite A026242 was used.

I think we can propose the (infinite(?)) BIP as entry in the OEIS, and
add the (so far conjectural) comment that the finite subsequence
[...,15,50] is obtained in case one uses the stronger sieve.

Regards,
Maximilian

On Wed, Sep 17, 2014 at 3:19 PM, M. F. Hasler <oeis at hasler.fr> wrote:
> I just need confirmation that the next term after the "pivots" (and
> thus "primes") 2,3,4,5  is not 6 nor 7 (both already underlined)
> but 8 which is the next non underlined term. (...)
> cf. http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes ;
> in particular the phrase
> "Next number *not yet crossed out* in the list after 3 is 5, ...".
>
> M.
>
> On Wed, Sep 17, 2014 at 1:54 PM, L. Edson Jeffery <lejeffery2 at gmail.com> wrote:
>> Maximilian,
>>
>> In Eric's sieve, as with the sieve of Eratosthenes, terms can be
>> underlined, circled or otherwise marked in some way but not removed
>> (erased, deleted, set to zero, etc.).
(...)