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A183072
Positive integers k such that 2^k - 1 is composite and each of its prime divisors has the form 4j + 3.
7
6, 10, 14, 15, 26, 30, 34, 38, 43, 51, 62, 65, 79, 85, 86, 93, 95, 122, 129, 130, 133, 158, 170, 193, 254, 255, 301, 311, 331, 349, 389, 445, 557, 577, 579, 631, 647, 1103, 1167
OFFSET
1,1
COMMENTS
Needed factorizations are in the Cunningham Project.
FORMULA
A183076(n) = 2^a(n) - 1.
EXAMPLE
6 is in this sequence because 2^6 - 1 = 3^2 * 7, and 3 and 7 have the form 4j + 3.
MATHEMATICA
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 *)
KEYWORD
nonn,hard,more
AUTHOR
Stuart Clary, Dec 23 2010
EXTENSIONS
a(38)-a(39) from Amiram Eldar, Feb 18 2019
STATUS
approved