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%I #11 Feb 18 2019 06:13:35
%S 43,79,193,311,331,349,389,557,577,631,647,1103
%N Prime numbers p such that 2^p - 1 is composite and each of its prime divisors has the form 4j + 3.
%C Needed factorizations are in the Cunningham Project.
%H S. S. Wagstaff, Jr., <a href="http://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>.
%F A183078(n) = 2^a(n) - 1.
%e 43 is in this sequence because 2^43 - 1 = 431 * 9719 * 2099863, and each of those primes has the form 4j + 3.
%t cQ[n_]:=Module[{x=2^n-1},!PrimeQ[x]&&Union[Mod[Transpose[ FactorInteger[ x]][[1]],4]]=={3}]; Select[Prime[Range[120]],cQ] (* _Harvey P. Dale_, Jun 17 2014 *)
%Y Cf. A000043, A136003, A183071, A183072, A183073.
%Y Cf. A000668, A136005, A183075, A183076, A183077, A183078.
%K nonn,hard
%O 1,1
%A _Stuart Clary_, Dec 23 2010
%E a(12) from _Amiram Eldar_, Feb 18 2019
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