NEW SEQUENCE: Semiprime gaps without primes

[Peter Pein]

Hi seqfans,

once again I overlooked a detail. Jaques Tramu wrote me that I did not
consider the function nextsemiprime. Of course 34=2*17 is a semiprime. So I've
been again totally wrong. Sorry for my inconsiderate posting.

With Mathematicas help i get now:

sp = Import["~/b001358.txt", "Table"][[All,2]]

Block[{n = 1, result = {}, tmp},
  While[(tmp = Select[sp,
       MemberQ[sp, #1 + n] &&
         And @@ (FreeQ[sp, #1] & ) /@
           Range[#1 + 1, #1 + n -
             1] && Select[Range[#1,
            #1 + n], PrimeQ, 1] ==
          {} & , 1]) != {},
    result = Join[result, tmp]; n++];
   result]

--> {9, 49, 62, 403, 341, 843, 6722, 3473,
  2869, 14059, 18467, 26603}

which is the start of Zak's sequence.

Peter


Peter Pein schrieb:
> Dear Zak and seqfans
> 
> propably I have got difficulties in understanding the definition.
> 
> I get 33 as a(2) because 33=3*11 and 33+2=7*5 and 34 is not prime.
> 
> Have a nice Christmas,
> Peter