A177216 Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3, 8*k-7, 16*k-15, 32*k-31, 64*k-63 and 128*k-127 are also products of two distinct primes.

11293, 12139, 25399, 31261, 36199, 44869, 49471, 62521, 72397, 83086, 89737, 91705, 98941, 124846, 125041, 134023, 138994, 144793, 164041, 166171, 170431, 173311, 182527, 199543, 224962, 244294, 258169, 259891, 263086, 275281, 277987

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 04 2010

Keywords

• nonn

Examples

			11293 is a term because 11293 = 23*491, 2*11293 - 1 = 22585 = 5*4517, 4*11293 - 1 = 45169 = 17*2657, 8*11293 - 1 = 90337 = 13*6949, 16*11293 - 1 = 180673 = 79*2287, 32*11293 - 1 = 361345 = 5*72269, 64*11293 - 1 = 722689 = 11*65699, and 128*11293 - 1 = 1445377 = 193*7489.
		

Crossrefs

Cf. A006881, A177210, A177211, A177212, A177213, A177214, A177215.

Programs

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1,1}; lst={};Do[If[f[n]&&f[2*n-1]&&f[4*n-3]&&f[8*n-7]&&f[16*n-15]&&f[32*n-31]&&f[64*n-63]&&f[128*n-127],AppendTo[lst,n]],{n,11293,4*9!}];lst
tdpQ[n_]:=Module[{f=Table[n*2^i-(2^i-1),{i,0,7}]},And@@(Transpose[ FactorInteger[ #]][[2]]=={1,1}&/@f)]; Select[Range[300000],tdpQ] (* Harvey P. Dale, Apr 02 2015 *)

Extensions

Example moved from Comments field to Example field by Harvey P. Dale, Apr 02 2015