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A275508
First occurrence of a run of exactly n consecutive integers with an even number of prime factors.
1
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
1,2
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
Sequence in context: A229543 A175201 A066793 * A139055 A294030 A079625
KEYWORD
nonn
AUTHOR
G. L. Honaker, Jr., Jul 30 2016
EXTENSIONS
a(11)-a(30) from Charles R Greathouse IV, Jul 30 2016
STATUS
approved