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Old 2005-01-27, 14:52   #2
Jean Penné
 
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May 2004
FRANCE

56010 Posts
Default How did you choose the candidate k values ?

I wish to ask some questions about the choose you made of the candidate
k values :

let N = k*4^n +1 with k odd.

I wish to compute N modulo 3.

4 = 1 (mod 3), so 4^n = 1 (mod 3)

so, N = k+1 (mod 3) All the possibilities are here :

k = 0 (mod 3) ==> N = 1 (mod 3)
k = 1 (mod 3) ==> N = 2 (mod 3)
k = 2 (mod 3) ==> N = 0 (mod 3), so these k's are all Sierpinski base 4 !!

Without any restriction on the k values, the "Sierpinski base 4" problem
would be rather trivial, because the least Sierpinki would be k = 5!

( I verified that with Newpgen...)

So, I understand why you added the condition 3 | k in your definition...
But why do you also exclude k = 1 (mod 3) ? Perhaps to avoid the values
already taken by Seventeen or Bust project, am I wrong ?

Regards,
Jean
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