A114404 4-almost prime gaps. First differences of A014613.

8, 12, 4, 14, 2, 4, 21, 3, 4, 2, 10, 4, 22, 6, 3, 1, 4, 10, 2, 4, 28, 5, 7, 2, 6, 6, 10, 5, 3, 4, 2, 14, 2, 10, 16, 18, 2, 1, 9, 2, 7, 13, 2, 10, 2, 2, 4, 2, 1, 13, 8, 3, 1, 4, 10, 24, 10, 17, 3, 15, 1, 2, 10, 4, 8, 4, 2, 2, 3, 15, 3, 3, 6, 3, 7, 4, 10, 4, 8, 6, 4, 2, 2, 8, 4, 1, 35, 1, 4, 7, 4, 8, 6

Offset: 1

Author

Jonathan Vos Post, Nov 25 2005

Keywords

• easy
• nonn

Examples

			a(1) = 8 = 24-16 where 16 is the first 4-almost prime and 24 is the second.
a(2) = 12 = 36-24.
a(3) = 4 = 40-36.
a(4) = 14 = 54-40.
a(5) = 2 = 56-54.
a(6) = 4 = 60-56.
a(7) = 21 = 81-60.
a(13) = 22 = 126-104.
a(21) = 28 = 184-156.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A014613, A065516, A111870, A111871, A114403-A114411, A114412-A114422.

Programs

Maple

A114404 := proc(nmax) local a,i,a014613 ; a := [] ; i := 1 ; a014613 := -1 ; while nops(a) < nmax do if numtheory[bigomega](i) = 4 then if a014613 > 0 then a := [op(a),i-a014613] ; fi ; a014613 := i ; fi ; i := i+1 ; end: a ; end: A114404(200) ; # R. J. Mathar, May 10 2007

Mathematica

Differences[Select[Range[800],Total[FactorInteger[#][[All,2]]]==4&]] (* Harvey P. Dale, Feb 14 2017 *)
Select[Range[1000],PrimeOmega[#]==4&]//Differences (* Harvey P. Dale, May 12 2018 *)

Formula

a(n) = A014613(n+1) - A014613(n).

Extensions

Corrected and extended by R. J. Mathar, May 10 2007