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%I #18 Feb 18 2019 06:04:59
%S 2,3,5,7,13,17,19,31,43,61,79,89,107,127,193,311,331,349,389,521,557,
%T 577,607,631,647,1103
%N Prime numbers p such that each prime divisor of 2^p - 1 has the form 4j + 3.
%C The exponents of the Mersenne primes (A000043) are contained in this sequence.
%C Needed factorizations are in the Cunningham Project.
%C Also in the sequence are 1279, 2203, 2281, 2909, 3217, 4253. - _Amiram Eldar_, Feb 18 2019
%H S. S. Wagstaff, Jr., <a href="http://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>.
%F A183077(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 Select[Prime[Range[30]],And@@(IntegerQ[(#-3)/4]&/@Transpose[ FactorInteger[ 2^#-1]][[1]])&] (* Increase the value of Range to increase the number of terms generated, but processing times grow very quickly as the value increases. *)(* _Harvey P. Dale_, Jan 01 2013 *)
%Y Cf. A000043, A136003, A183071, A183072, A183074.
%Y Cf. A000668, A136005, A183075, A183076, A183077, A183078.
%K nonn,hard,more
%O 1,1
%A _Stuart Clary_, Dec 23 2010
%E a(26) from _Amiram Eldar_, Feb 18 2019