A183072 Positive integers k such that 2^k - 1 is composite and each of its prime divisors has the form 4j + 3.

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

Author

Stuart Clary, Dec 23 2010

Keywords

• nonn
• hard
• more

Comments

Needed factorizations are in the Cunningham Project.

Examples

			6 is in this sequence because 2^6 - 1 = 3^2 * 7, and 3 and 7 have the form 4j + 3.
		

Links

• S. S. Wagstaff, Jr., The Cunningham Project.

Crossrefs

Cf. A000043, A136003, A183071, A183073, A183074.

Cf. A000668, A136005, A183075, A183076, A183077, A183078.

Programs

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 *)

Formula

A183076(n) = 2^a(n) - 1.

Extensions

a(38)-a(39) from Amiram Eldar, Feb 18 2019