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

1,1

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A070477 A070697 A004473 * A173457 A033198 A072900

Adjacent sequences: A114401 A114402 A114403 * A114405 A114406 A114407

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 25 2005

Extensions

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

Status

approved