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%I #18 Feb 26 2020 11:49:23
%S 2,2,2,3,7,13,19,37,757,111779,670669,6371347,34204069,166437443,
%T 310854619,385634101,14188652209,42594124681,10825536799379161,
%U 154680726732318637
%N Successive prime factors of (3^1006003 - 3)/1006003^2.
%C 1006003 = A014127(2).
%C 2 is the only prime that occurs to a power greater than 1.
%C Conjecture (*Artur Jasinski*): If another infinite sequences with good Hall's examples occurred, it would have to contain primes from this sequence as constant divisors of the whole sequence, because parts of Danilov's infinite sequence (A200216, A200217, A200218) contain divisors of (3^A014127(1) - 3)/(A014127(1)^2).
%C a(21) > 10^18. - _Max Alekseyev_, Feb 26 2020
%H FactorDB, <a href="http://factordb.com/index.php?query=3%5E1006002+-+1">Factorization of 3^1006002 - 1</a>.
%Y Cf. A014127.
%K nonn,fini,more
%O 1,1
%A _Artur Jasinski_, Nov 24 2011
%E More terms from _Sean A. Irvine_, Sep 06 2012
%E a(19)-a(20) from _Max Alekseyev_, Feb 13 2020
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