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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A124096 A308784 A142796 * A142020 A044234 A044615

Adjacent sequences: A201144 A201145 A201146 * A201148 A201149 A201150

Keyword

nonn

Author

Antonio Roldán, Nov 27 2011

Status

approved