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A123201 Numbers n such that factorizations of n..n+7 have same number of primes (including multiplicities). 4

%I

%S 3405122,3405123,6612470,8360103,8520321,9306710,10762407,12788342,

%T 12788343,15212151,15531110,16890901,17521382,17521383,21991382,

%U 21991383,22715270,22715271,22841702,22841703,22914722,22914723

%N Numbers n such that factorizations of n..n+7 have same number of primes (including multiplicities).

%C 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).

%H Donovan Johnson, <a href="/A123201/b123201.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 (PARI) c=0; p1=0; for(n=2, 10^8, p2=bigomega(n); if(p1==p2, c++; if(c>=7, print1(n-7 ",")), c=0; p1=p2)) /* _Donovan Johnson_, Mar 20 2013 */

%Y Cf. A045940, A045941, A045942, A123103.

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 05 2006

%E a(7)-a(22) from _Donovan Johnson_, Apr 09 2010

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Last modified May 13 00:11 EDT 2021. Contains 343829 sequences. (Running on oeis4.)