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.

247, 249, 295, 395, 422, 478, 493, 502, 519, 589, 634, 694, 721, 755, 955, 1255, 1267, 1294, 1306, 1351, 1387, 1441, 1522, 1546, 1727, 1762, 1942, 2031, 2119, 2155, 2323, 2374, 2449, 2491, 2509, 2533, 2587, 2623, 2661, 2733, 2773, 3005, 3039, 3091, 3334

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, and 8*247 - 1 = 1969 = 11*179.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006881, A177210, A177211.

Programs

Maple

isA006881:= proc(n) local F;
  F:= ifactors(n)[2];
  nops(F)=2 and F[1,2]+F[2,2]=2
end proc:
filter:= n -> andmap(isA006881, [n,2*n-1,4*n-3,8*n-7]);
select(filter, [$1..10000]); # Robert Israel, Jul 11 2017

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],AppendTo[lst,n]],{n,0,3*7!}];lst
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 *)