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 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. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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

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Last modified May 16 14:07 EDT 2021. Contains 343947 sequences. (Running on oeis4.)