Errors in A068232-A068235

[Adorján Ferenc]

On 5/17/06, franktaw at netscape.net <franktaw at netscape.net> wrote:

>    These are sequences of the first prime which starts a
sequence of n >consecutive primes that are congruent to a
particular value mod 12.
>     
>   The problem is that the programs (both Mathematica and
PARI) >assume that a(n+1) > a(n); whereas in fact  it is
possible that a(n+1) >= a(n).  I haven't done a thorough
check, but for A068232, we should >have a(8) = a(7) = 7790917.
     

Well, yes and no...

You are right that a(8) = a(7) = 7790917, as it is correctly
given in the sequence. But, - at least for the PARI code -
the code also gives the correct repetition. The trick is
that at the end of the PARI code you can see: ...
print(prime(i)); n++, i++) , where the "," comma separates
in a PARI if(condition,action if true,else) structure the
"action if true" block from the "else" block. Thus, "i" is
incremented only if there was no hit.

At the time of submitting those sequences I pondered
creating sequences of the positions of the first double,
triple, etc. elements, but was unable to create even 3
subsequent terms (there are no triples below the index of
10^7 primes).

Ferenc Adorjan



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