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The start of a record-breaking run of consecutive integers with an even number of prime factors.
4

%I #15 Sep 06 2022 13:25:14

%S 1,9,14,33,54,140,213,1934,35811,38405,200938,389409,1792209,5606457,

%T 8405437,68780189,880346227,85910903650,87635944146,284340107954,

%U 2195312273836,2864568747364,3155591650029

%N The start of a record-breaking run of consecutive integers with an even number of prime factors.

%C a(21) > 10^12. [From _Donovan Johnson_, Oct 11 2010]

%C a(24) > 10^13. - _Giovanni Resta_, Aug 01 2013

%C Prime factors counted with multiplicity. - _Harvey P. Dale_, Sep 06 2022

%t Table[SequencePosition[If[EvenQ[#],1,0]&/@PrimeOmega[Range[40000]],PadRight[{},n,1],1][[All,1]],{n,14}]//Flatten//Union (* The program generates the first 10 terms of the sequence. *) (* _Harvey P. Dale_, Sep 06 2022 *)

%Y Cf. A066794, A175201.

%K nonn

%O 1,2

%A _G. L. Honaker, Jr._, Jan 18 2002

%E Except for first 4 or 5 terms, computed by _Shyam Sunder Gupta_, Jan 26 2002

%E a(12) and a(14) corrected and a(18)-a(20) from _Donovan Johnson_, Oct 11 2010

%E a(21)-a(23) from _Giovanni Resta_, Aug 01 2013