[seqfan] Re: Biprimes of K

[M. F. Hasler]

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

(PARI) (ugly, only for my records...)
M=Mat([vector(90,n,n)~,A026242[1..90]~])~
do(k)=forstep(i=k+M[2,k],#M,M[2,k],M[2,i]=0);M
comp(A,B)=setminus(Set(A[2,1..#A]),Set(B[2,1..#B]))
do(3) \\ "uses" 2 => %1

do(4) \\ "uses" 3 => %2
[1 1 2 3 0 4 0 5 0 0 0 8 0 9 0 0 0 7 0 8 0 0 0 15 0 10 0 0 0 19 0 20 0
0 0 14 0 24 0 0 0 26 0 17 0 0 0 30 0 31 0 0 0 21 0 35 0 0 0 23 0 24 0
0 0 41 0 26 0 0 0 45 0 46 0 0 0 30 0 50 0 0 0 52 0 33 0 0 0 56]

comp(%1,%2) \\ numbers eliminated in this step:
% = [11, 13, 25, 27, 29, 36, 40, 47, 51, 55]

do(6) \\ "uses" 4 => %6
[1 1 2 3 0 4 0 5 0 0 0 8 0 0 0 0 0 0 0 8 0 0 0 15 0 0 0 0 0 0 0 20 0 0
0 14 0 0 0 0 0 0 0 17 0 0 0 30 0 0 0 0 0 0 0 35 0 0 0 23 0 0 0 0 0 0 0
26 0 0 0 45 0 0 0 0 0 0 0 50 0 0 0 52 0 0 0 0 0 0]

comp(%2,%6) \\ numbers eliminated in this step:
% = [7, 9, 10, 19, 21, 24, 31, 33, 41, 46, 56]

do(8) \\ "uses" 5 => %8
[1 1 2 3 0 4 0 5 0 0 0 8 0 0 0 0 0 0 0 8 0 0 0 15 0 0 0 0 0 0 0 20 0 0
0 14 0 0 0 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 35 0 0 0 23 0 0 0 0 0 0 0
0 0 0 0 45 0 0 0 0 0 0 0 50 0 0 0 52 0 0 0 0 0 0]

comp(%6,%8) \\ numbers eliminated in this step:
% = [26, 30]