A201220 Numbers m such that m, m-1, m-2 and m-3 are 1,2,3,4-almost primes respectively.

107, 263, 347, 479, 863, 887, 1019, 2063, 2447, 3023, 3167, 3623, 5387, 5399, 5879, 6599, 6983, 7079, 8423, 8699, 9743, 9887, 10463, 11807, 12263, 12347, 14207, 15383, 15767, 18959, 20663, 22343, 23039, 23567, 24239, 27239, 32183, 33647, 33767, 37799

Offset: 1

Author

Antonio Roldán, Nov 28 2011

Keywords

• nonn

Comments

Following a suggestion of Claudio Meller.

m is of the form 12k-1, so m-2 is a multiple of 3 and m-3 is a multiple of 4.

Examples

			6599 is prime, 6598=2*3299 is semiprime, 6597=3*3*733 is 3-almost prime, 6596=2*2*17*97 is 4-almost prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1700

Crossrefs

Subsequence of A005385 and of A201147.

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

Programs

Mathematica

primeCount[n_] := Plus @@ Transpose[FactorInteger[n]][[2]]; Select[Range[40000], primeCount[#] == 1 && primeCount[#-1] == 2 && primeCount[#-2] == 3 && primeCount[#-3] == 4 &] (* T. D. Noe, Nov 28 2011 *)
Select[Range[40000],PrimeOmega[Range[#,#+3]]=={4,3,2,1}&]+3 (* Harvey P. Dale, Dec 10 2011 *)
SequencePosition[PrimeOmega[Range[40000]],{4,3,2,1}][[;;,2]] (* Harvey P. Dale, Oct 08 2023 *)

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) && bigomega(t-3)==4, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 02 2017