A177213 Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3, 8*k-7 and 16*k-15 are also products of two distinct primes.

247, 295, 478, 634, 694, 721, 1255, 1267, 1294, 1387, 1546, 1762, 1942, 2323, 2374, 2773, 3005, 3334, 3403, 3883, 3949, 4126, 4714, 4741, 4777, 5062, 5269, 5287, 5353, 5422, 5617, 6583, 6805, 7273, 7495, 8587, 8767, 9017, 9406, 9427, 9847, 10018

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 04 2010

Keywords

• nonn

Examples

			247 is a term because 247 = 13*19, 2*247 - 1 = 493 = 17*29, 4*247 - 3 = 985 = 5*197, 8*247 - 1 = 1969 = 11*179, and 16*247 - 15 = 3937 = 31*127.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006881, A177210, A177211, A177212.

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],AppendTo[lst,n]],{n,0,8!}];lst
ptdpQ[n_]:=PrimeNu[n]==PrimeOmega[n]==2; Select[Range[11000],AllTrue[ {#,2#-1,4#-3,8#-7,16#-15},ptdpQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 30 2016 *)