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

1,1

Links

Table of n, a(n) for n=1..31.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A195649 A110375 A252859 * A112441 A104017 A317400

Adjacent sequences: A177213 A177214 A177215 * A177217 A177218 A177219

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2010

Extensions

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

Status

approved