%I #13 Feb 18 2019 09:57:31
%S 6,10,14,15,26,30,34,38,43,51,62,65,79,85,86,93,95,122,129,130,133,
%T 158,170,193,254,255,301,311,331,349,389,445,557,577,579,631,647,1103,
%U 1167
%N Positive integers k such that 2^k - 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 A183076(n) = 2^a(n) - 1.
%e 6 is in this sequence because 2^6 - 1 = 3^2 * 7, and 3 and 7 have the form 4j + 3.
%t c4j3Q[n_]:=Module[{c=2^n-1},CompositeQ[c]&&AllTrue[(#-3)/4&/@ FactorInteger[ c] [[All,1]],IntegerQ]]; Select[Range[650],c4j3Q] (* Requires Mathematica version 10 or later *) (* The program takes a long time to run *) (* _Harvey P. Dale_, Sep 23 2018 *)
%Y Cf. A000043, A136003, A183071, A183073, A183074.
%Y Cf. A000668, A136005, A183075, A183076, A183077, A183078.
%K nonn,hard,more
%O 1,1
%A _Stuart Clary_, Dec 23 2010
%E a(38)-a(39) from _Amiram Eldar_, Feb 18 2019