login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)