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A114403 3-almost prime gaps. First differences of A014612. 23
4, 6, 2, 7, 1, 2, 12, 2, 1, 5, 2, 11, 3, 2, 2, 5, 1, 2, 14, 6, 1, 3, 3, 5, 4, 2, 1, 7, 1, 5, 8, 9, 1, 5, 1, 10, 1, 5, 1, 1, 2, 1, 7, 4, 2, 2, 5, 12, 5, 10, 8, 1, 5, 2, 4, 2, 1, 1, 9, 3, 3, 5, 2, 5, 2, 4, 3, 2, 1, 1, 4, 2, 18, 6, 2, 4, 3, 7, 1, 5, 5, 2, 9, 2, 1 (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) = A014612(n+1) - A014612(n).

EXAMPLE

a(1) = 4 = 12-8 where 8 is the first 3-almost prime and 12 is the second.

a(2) = 6 = 18-12

a(3) = 2 = 20-18

a(4) = 7 = 27-20

MAPLE

is3Alm := proc(n::integer) local ifa, ex, i ; ifa := op(2, ifactors(n)) ; ex := 0 ; for i from 1 to nops(ifa) do ex := ex+ op(2, op(i, ifa)) ; od : if ex = 3 then RETURN(true) ; else RETURN(false) ; fi ; end: A014612 := proc(n::integer) local resul, i; i :=1; resul := 8 ; while i < n do resul := resul + 1 ; if is3Alm(resul) then i := i+1 ; fi ; od ; RETURN(resul) ; end: A114403 := proc(n::integer) RETURN(A014612(n+1)-A014612(n)) ; end: for n from 1 to 160 do printf("%d, ", A114403(n)) ; od: # R. J. Mathar, Apr 25 2006

MATHEMATICA

Differences[Select[Range[425], PrimeOmega[#] == 3 &]] (* Jayanta Basu, Jul 01 2013 *)

CROSSREFS

Cf. A014612, A065516, A111870, A111871, A114403-A114411, A114412-A114422.

Sequence in context: A029677 A045867 A236189 * A137662 A153124 A066252

Adjacent sequences:  A114400 A114401 A114402 * A114404 A114405 A114406

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 25 2005

EXTENSIONS

Corrected and extended by R. J. Mathar, Apr 25 2006

STATUS

approved

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Last modified August 18 20:11 EDT 2017. Contains 290762 sequences.