login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "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 A336049 A153124

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 3 05:29 EST 2020. Contains 338899 sequences. (Running on oeis4.)