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The smallest odd prime factor of the Lucas-Lehmer number A003010(n).
2

%I #20 Apr 03 2023 10:36:12

%S 7,97,31,708158977,127,22783,113210499946729046527,12289,

%T 1049179854847,22427452848394140276947044397991663611794141183,8191,

%U 29687809

%N The smallest odd prime factor of the Lucas-Lehmer number A003010(n).

%C Does this sequence include all of the Mersenne primes greater than 3?

%C a(8)=12289; a(11)=8191, a(15)=131071.

%C Also the least prime factor of A002812(n). - _Michel Marcus_, Dec 16 2022

%C a(p-2) = 2^p-1 for all odd Mersenne exponents p in A000043? - _Thomas Ordowski_, Aug 12 2018

%H Chris Caldwell, <a href="https://t5k.org/mersenne/index.html">Mersenne primes</a>

%e A003010(3)=37634 and its smallest odd prime factor is 31.

%Y Cf. A000040, A003010, A000668, A002812.

%K nonn,more

%O 1,1

%A _G. L. Honaker, Jr._, Dec 13 2010

%E More terms, using factordb, from _Michel Marcus_ and _Hugo Pfoertner_, Dec 16 2022