A209292 - OEIS

%I #18 Jan 17 2013 15:37:00

%S 1,2,3,5,8,11,13,18,20,23,29,30,31,36,37,40,41,44,48,50,52,53,54,56,

%T 63,67,68,73,75,76,78,81,83,89,90,96,97,98,99,103,105,112,113,114,116,

%U 120,125,127,128,130,131,135,136,137,138,139,140,148,153,156

%N Non-semiprimes n such that 2n+1 are non-semiprimes.

%C This is to A005384 as nonsemiprimes A100959 are to primes A000040.

%F {n such that n is in A100959, and 2*n + 1 is in A100959} = {n such that n is not in A001358, and 2*n + 1 is not in A001358}.

%F a(n) ~ n. - _Charles R Greathouse IV_, Jan 16 2013

%e a(1) = 1 because 1 is not a semiprime (the smallest semiprime is 4), and 2*1 + 1 = 3 is not a semiprime.

%e 7 is not a semiprime, but 2*7 + 1 = 15 = 3*5 is a semiprime, so 7 is not in this sequence.

%t SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Range[200], ! SemiPrimeQ[#] && ! SemiPrimeQ[2 # + 1] &] (* _T. D. Noe_, Jan 17 2013 *)

%o (PARI) is(n)=bigomega(n)!=2 && bigomega(2*n+1)!=2 \\ _Charles R Greathouse IV_, Jan 16 2013

%Y Cf. A001358, A005384, A100959, A209271.

%K nonn,easy

%O 1,2

%A _Jonathan Vos Post_, Jan 16 2013