[seqfan] A283364 and a Diophantine equation

Vladimir Shevelev shevelev at bgu.ac.il
Tue Mar 7 14:28:40 CET 2017

Dear SeqFans,

Yesterday I submitted A283364:
 Numbers n such that both numbers 2^n+-1
have <=2 distinct prime factors. I proved
that the terms >9 are prime.

To-day I proved that the sequence coincides
with "Numbers n such that 2^n-1 has <=2
distinct prime factors" if and only if the 
Diophantine equation
2^(p^2) - 1 = (2^p-1)*q^k
has no solutions for 2^p-1 and q  prime
and integer k>=2.
Did anyone meet this equation? 

Best regards,

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