A201147 Numbers m such that m, m-1 and m-2 are 1,2,3-almost primes respectively.

47, 107, 167, 263, 347, 359, 467, 479, 563, 863, 887, 983, 1019, 1187, 1283, 1907, 2039, 2063, 2099, 2447, 2819, 2879, 3023, 3167, 3203, 3623, 3803, 3947, 4139, 4919, 5387, 5399, 5507, 5879, 6599, 6659, 6983, 7079, 7187, 7523, 7559, 7703, 8423, 8699, 8963

Offset: 1

Author

Antonio Roldán, Nov 27 2011

Keywords

• nonn

Comments

m-2 is multiple of 3.

m is of the form 12k-1.

This sequence is subset of A005385.

Following a suggestion of Claudio Meller.

Examples

			2099 is prime, 2098=2*1049 is semiprime, 2097=3*3*233 is 3-almost prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..8400

Crossrefs

Cf. A005385, A005383, A112998, A113000, A113008, A072875, A093552.

Programs

Mathematica

primeCount[n_] := Plus @@ Transpose[FactorInteger[n]][[2]]; Select[Range[10000], primeCount[#] == 1 && primeCount[#-1] == 2 && primeCount[#-2] == 3 &] (* T. D. Noe, Nov 28 2011 *)
Select[Range[10000],PrimeOmega[Range[#,#+2]]=={3,2,1}&]+2 (* Harvey P. Dale, Dec 10 2011 *)

PARI

list(lim)=my(v=List(),L=(lim-2)\3,t); forprime(p=3,L\3, forprime(q=3,min(p,L\p), t=3*p*q+2; if(isprime(t) && isprime((t-1)/2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017