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A177212 Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3 and 8*k-7 are also products of two distinct primes.

%I A177212 #14 Feb 16 2021 02:10:44
%S A177212 247,249,295,395,422,478,493,502,519,589,634,694,721,755,955,1255,
%T A177212 1267,1294,1306,1351,1387,1441,1522,1546,1727,1762,1942,2031,2119,
%U A177212 2155,2323,2374,2449,2491,2509,2533,2587,2623,2661,2733,2773,3005,3039,3091,3334
%N A177212 Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3 and 8*k-7 are also products of two distinct primes.
%H A177212 Robert Israel, <a href="/A177212/b177212.txt">Table of n, a(n) for n = 1..10000</a>
%e A177212 247 is a term because 247 = 13*19, 2*247 - 1 = 493 = 17*29, 4*247-3 = 985 = 5*197, and 8*247 - 1 = 1969 = 11*179.
%p A177212 isA006881:= proc(n) local F;
%p A177212   F:= ifactors(n)[2];
%p A177212   nops(F)=2 and F[1,2]+F[2,2]=2
%p A177212 end proc:
%p A177212 filter:= n -> andmap(isA006881, [n,2*n-1,4*n-3,8*n-7]);
%p A177212 select(filter, [$1..10000]); # _Robert Israel_, Jul 11 2017
%t A177212 f[n_]:=Last/@FactorInteger[n]=={1,1}; lst={};Do[If[f[n]&&f[2*n-1]&&f[4*n-3]&&f[8*n-7],AppendTo[lst,n]],{n,0,3*7!}];lst
%t A177212 p2dpQ[n_]:=Transpose[FactorInteger[n]][[2]]=={1,1}; With[{s=Select[Range[ 3500], p2dpQ]},Select[s,AllTrue[{2#-1,4#-3,8#-7},p2dpQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 27 2015 *)
%Y A177212 Cf. A006881, A177210, A177211.
%K A177212 nonn
%O A177212 1,1
%A A177212 _Vladimir Joseph Stephan Orlovsky_, May 04 2010