The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #12 Jul 01 2022 19:37:59
%S 1,9,14,33,54,201,140,2170,213,4529,10403,1934,35811,162144,38405,
%T 414225,200938,389409,1792209,5606457,18493931,30947532,61190563,
%U 8405437,203631499,577699919,158280474,68780189,4082994208,3944563444
%N First occurrence of a run of exactly n consecutive integers with an even number of prime factors.
%e a(3)=14 because 14 begins the first occurrence of a run of exactly 3 consecutive integers with an even number of prime factors, i.e., 14=2*7, 15=3*5, 16=2*2*2*2.
%t Join[{1},Table[SequencePosition[Table[If[EvenQ[PrimeOmega[n]],1,0],{n,5610000}],Join[ {0},PadRight[{},d,1],{0}],1],{d,2,20}][[All,1,1]]+1] (* The program generates the first 20 terms of the sequence. *) (* _Harvey P. Dale_, Jul 01 2022 *)
%o (PARI) v=vector(100); last=0; for(n=1,1e10, if(bigomega(n)%2, t=n-last-1; if(t && v[t]==0, v[t]=n-t; print(t" "n-t)); last=n)) \\ _Charles R Greathouse IV_, Jul 30 2016
%Y Cf. A005843, A066829.
%K nonn
%O 1,2
%A _G. L. Honaker, Jr._, Jul 30 2016
%E a(11)-a(30) from _Charles R Greathouse IV_, Jul 30 2016