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

1,2

Links

Table of n, a(n) for n=1..30.

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

Cf. A005843, A066829.

Sequence in context: A229543 A175201 A066793 * A139055 A294030 A079625

Adjacent sequences: A275505 A275506 A275507 * A275509 A275510 A275511

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