A275508 First occurrence of a run of exactly n consecutive integers with an even number of prime factors.
1, 9, 14, 33, 54, 201, 140, 2170, 213, 4529, 10403, 1934, 35811, 162144, 38405, 414225, 200938, 389409, 1792209, 5606457, 18493931, 30947532, 61190563, 8405437, 203631499, 577699919, 158280474, 68780189, 4082994208, 3944563444
Offset: 1
Keywords
Examples
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.
Programs
-
Mathematica
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 *) -
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
Extensions
a(11)-a(30) from Charles R Greathouse IV, Jul 30 2016