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A140079 Numbers n such that n and n+1 have 5 distinct prime factors. 11

%I

%S 254540,310155,378014,421134,432795,483405,486590,486794,488565,

%T 489345,507129,522444,545258,549185,558789,558830,567644,577940,

%U 584154,591260,598689,627095,634809,637329,663585,666995,667029,678755,687939,690234

%N Numbers n such that n and n+1 have 5 distinct prime factors.

%C For the smallest number r such that r and r+1 have n distinct prime factors, see A093548.

%C Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite. - _Charles R Greathouse IV_, Jun 02 2016

%C Subsequence of the variant A321505 defined with "at least 5" instead of "exactly 5" distinct prime factors. See A321495 for the differences. - _M. F. Hasler_, Nov 12 2018

%H Seiichi Manyama, <a href="/A140079/b140079.txt">Table of n, a(n) for n = 1..10000</a>

%H D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yildirim., <a href="https://arxiv.org/abs/0803.2636">Small gaps between almost primes, the parity problem and some conjectures of Erdos on consecutive integers</a>, arXiv:0803.2636 [math.NT], 2008.

%t a = {}; Do[If[Length[FactorInteger[n]] == 5 && Length[FactorInteger[n + 1]] == 5, AppendTo[a, n]], {n, 1, 100000}]; a (*Artur Jasinski*)

%t Transpose[SequencePosition[Table[If[PrimeNu[n]==5,1,0],{n,700000}],{1,1}]][[1]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 25 2015 *)

%o (PARI) is(n)=omega(n)==5 && omega(n+1)==5 \\ _Charles R Greathouse IV_, Jun 02 2016

%Y Cf. A074851, A140077, A140078.

%Y Cf. A093548.

%Y Equals A321505 \ A321495.

%K nonn

%O 1,1

%A _Artur Jasinski_, May 07 2008

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Last modified July 7 13:44 EDT 2020. Contains 335495 sequences. (Running on oeis4.)