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%I #20 Feb 08 2024 10:40:33
%S 3,5,7,17,19,89,107,521,2203,2281,4253
%N Primes p such that 2^p - 1 is a prime with primitive root 3.
%C If A096393(n) = 3, then A000043(n) belongs to this sequence.
%C 2^a(n) - 1 is in A001123.
%C a(12) >= 21701. - _Max Alekseyev_, Feb 08 2024
%H Discussion titled <a href="http://www.mersenneforum.org/showthread.php?t=5874">Conjecture about multiplicative order of 3 modulo a Mersenne prime</a>, (postings in mersenneforum.org), starting May 14 2006.
%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%t Select[Prime@Range[98], PrimitiveRoot[2^# - 1] == 3 &]
%Y Subsequence of A000043.
%Y Cf. A001123, A096393.
%K hard,more,nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Nov 20 2012
%E a(9)-a(11) from _Max Alekseyev_, Feb 07 2024