cp's OEIS Frontend

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

%I A140079 #36 Jul 19 2023 08:01:55
%S A140079 254540,310155,378014,421134,432795,483405,486590,486794,488565,
%T A140079 489345,507129,522444,545258,549185,558789,558830,567644,577940,
%U A140079 584154,591260,598689,627095,634809,637329,663585,666995,667029,678755,687939,690234
%N A140079 Numbers n such that n and n+1 have 5 distinct prime factors.
%C A140079 For the smallest number r such that r and r+1 have n distinct prime factors, see A093548.
%C A140079 Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite. - _Charles R Greathouse IV_, Jun 02 2016
%C A140079 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
%C A140079 The subset of numbers where n and n+1 are also squarefree gives A318964. - _R. J. Mathar_, Jul 15 2023
%H A140079 Seiichi Manyama, <a href="/A140079/b140079.txt">Table of n, a(n) for n = 1..10000</a>
%H A140079 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.
%F A140079 {k: k in A051270 and k+1 in A051270}. - _R. J. Mathar_, Jul 19 2023
%t A140079 a = {}; Do[If[Length[FactorInteger[n]] == 5 && Length[FactorInteger[n + 1]] == 5, AppendTo[a, n]], {n, 1, 100000}]; a (*Artur Jasinski*)
%t A140079 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 A140079 (PARI) is(n)=omega(n)==5 && omega(n+1)==5 \\ _Charles R Greathouse IV_, Jun 02 2016
%Y A140079 Cf. A074851, A140077, A140078, A273897.
%Y A140079 Cf. A093548.
%Y A140079 Equals A321505 \ A321495.
%K A140079 nonn
%O A140079 1,1
%A A140079 _Artur Jasinski_, May 07 2008