n..n+6 are all N-almost primes

[zak seidov]

--- zak seidov <zakseidov at yahoo.com> wrote:
> Are there longer set(s) of successive numbers
> n..n+m (m>6)
> which are products of the same number (N) of primes
> (including multiplicities)?

Me: Just submitted:
%I A000001
%S A000001
3405122,3405123,6612470,8360103,8520321,9306710
%N A000001 Numbers n such that n..n+7 are products of
the same number of primes.
%C A000001 Note that because 3405130=2*5*167*2039 is
also 4-almost prime,
3405122 is the first n such that numbers n..n+8 are
products of the same number N of primes (N=4).
%e A000001 3405122=2*7*29*8387, 3405123=3^2*19*19913,
3405124=2^2*127*6703, 3405125=5^3*27241,
3405126=2*3*59*9619, 3405127=11*23*43*313,
3405128=2^3*425641, 3405129=3*7*13*12473 all 4-almost
primes.
%O A000001 1
%K A000001 ,nonn,
%A A000001 Zak Seidov  (zakseidov at yahoo.com), Nov 05
2006

Now we need to find numbers n such that n..n+m (m>8)
are N-almost primes (n'd be >10^7).

Thanks, Zak

BTW The "annoying" ad at the bottom of message is 
from Yahoo!Mail - not me, sorry.

<original message>
> Just dubmitted.
> 
> My Q to gurus:
> Are there longer set(s) of successive numbers
> n..n+m (m>6)
> which are products of the same number (N) of primes
> (including multiplicities)?
> 
> It seems that for  larger N's, 
> the larger m's may be(?).
> 
> Thanks, Zak
>   
> %I A000001
> %S A000001
>
211673,298433,355923,381353,460801,506521,540292,568729,690593,705953,737633,741305,921529
> %N A000001 Numbers n such that factorizations of
> n..n+6 have same number of primes (including
> multiplicities).
> %C A000001 Subset of A045940  Numbers n such that
> factorizations of n..n+3 have same number of primes
> (including multiplicities).
> %e A000001 211673=7*11*2749, 211674=2*3*35279,
> 211675=5^2*8467, 211676=2^2*52919, 211677=3*37*1907,
> 211677=2*109*971, 211679=13*19*857 all 3-almost
> primes;
> 355923=3^2*71*557, 355924=2^2*101*881,
> 355925=5^22*23*619, 355926=2*3*137*433,
> 355927=11*13*19*131, 355928=2^3*44491,
> 355929=3*7*17*997 all 4-almost primes.
> %Y A000001 A045940.
> %O A000001 1
> %K A000001 ,nonn,
> %A A000001 Zak Seidov  (zakseidov at yahoo.com), Nov 05
> 2006
> 




 
____________________________________________________________________________________
Access over 1 million songs - Yahoo! Music Unlimited 
(http://music.yahoo.com/unlimited)