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A114404 4-almost prime gaps. First differences of A014613. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)