A209292 Non-semiprimes n such that 2n+1 are non-semiprimes.

1, 2, 3, 5, 8, 11, 13, 18, 20, 23, 29, 30, 31, 36, 37, 40, 41, 44, 48, 50, 52, 53, 54, 56, 63, 67, 68, 73, 75, 76, 78, 81, 83, 89, 90, 96, 97, 98, 99, 103, 105, 112, 113, 114, 116, 120, 125, 127, 128, 130, 131, 135, 136, 137, 138, 139, 140, 148, 153, 156

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

{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}.

a(n) ~ n. - Charles R Greathouse IV, Jan 16 2013

Example

a(1) = 1 because 1 is not a semiprime (the smallest semiprime is 4), and 2*1 + 1 = 3 is not a semiprime.
7 is not a semiprime, but 2*7 + 1 = 15 = 3*5 is a semiprime, so 7 is not in this sequence.

Mathematica

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 *)

Prog

(PARI) is(n)=bigomega(n)!=2 && bigomega(2*n+1)!=2 \\ Charles R Greathouse IV, Jan 16 2013

Crossrefs

Cf. A001358, A005384, A100959, A209271.

Sequence in context: A246361 A228855 A171048 * A185371 A071894 A301892

Adjacent sequences: A209289 A209290 A209291 * A209293 A209294 A209295

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 16 2013

Status

approved