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%I #12 Feb 16 2021 02:11:12
%S 247,295,478,634,694,721,1255,1267,1294,1387,1546,1762,1942,2323,2374,
%T 2773,3005,3334,3403,3883,3949,4126,4714,4741,4777,5062,5269,5287,
%U 5353,5422,5617,6583,6805,7273,7495,8587,8767,9017,9406,9427,9847,10018
%N 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.
%H Harvey P. Dale, <a href="/A177213/b177213.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%t 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
%t 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 *)
%Y Cf. A006881, A177210, A177211, A177212.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 04 2010
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