A177221 Numbers k that are the products of two distinct primes such that 2*k + 1 is also the product of two distinct primes.

10, 34, 38, 46, 55, 57, 77, 91, 93, 106, 118, 123, 129, 133, 143, 145, 159, 161, 177, 185, 201, 203, 205, 206, 213, 218, 226, 235, 259, 267, 291, 295, 298, 305, 314, 327, 334, 335, 339, 358, 365, 377, 381, 394, 395, 403, 407, 415, 417, 446, 447, 458, 466, 469

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 05 2010

Keywords

• nonn

Examples

			10 is in the sequence because 10 = 2*5 and 2*10+1 = 21 = 3*7.
		

Links

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

Crossrefs

Cf. A006881, A111153, A177210, A177211, A177212, A177213, A177214, A177215, A177216, A177217, A177220.

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]); select(filter, [$1..1000]); # Robert Israel, Nov 09 2017

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1,1}; lst={};Do[If[f[n]&&f[2*n+1],AppendTo[lst,n]],{n,0,3*6!}];lst
Select[Range[500],PrimeNu[#]==PrimeOmega[#]==PrimeNu[2#+1] == PrimeOmega[ 2#+1] == 2&] (* Harvey P. Dale, Feb 22 2018 *)