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 A183074 Prime numbers p such that 2^p - 1 is composite and each of its prime divisors has the form 4j + 3. 7
 43, 79, 193, 311, 331, 349, 389, 557, 577, 631, 647, 1103 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Needed factorizations are in the Cunningham Project. LINKS S. S. Wagstaff, Jr., The Cunningham Project. FORMULA A183078(n) = 2^a(n) - 1. EXAMPLE 43 is in this sequence because 2^43 - 1 = 431 * 9719 * 2099863, and each of those primes has the form 4j + 3. MATHEMATICA 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 *) CROSSREFS Cf. A000043, A136003, A183071, A183072, A183073. Cf. A000668, A136005, A183075, A183076, A183077, A183078. Sequence in context: A121957 A118075 A236839 * A289730 A045238 A139982 Adjacent sequences:  A183071 A183072 A183073 * A183075 A183076 A183077 KEYWORD nonn,hard AUTHOR Stuart Clary, Dec 23 2010 EXTENSIONS a(12) from Amiram Eldar, Feb 18 2019 STATUS approved

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Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)