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