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%I A140078 #37 Jun 20 2024 18:00:59
%S A140078 7314,8294,8645,9009,10659,11570,11780,11934,13299,13629,13845,14420,
%T A140078 15105,15554,16554,16835,17204,17390,17654,17765,18095,18290,18444,
%U A140078 18920,19005,19019,19095,19227,20349,20405,20769,21164,21489,21735
%N A140078 Numbers k such that k and k+1 have 4 distinct prime factors.
%C A140078 Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite. - _Charles R Greathouse IV_, Jun 02 2016
%C A140078 The subsequence of terms where k and k+1 are also squarefree is A318896. - _R. J. Mathar_, Jul 15 2023
%D A140078 David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 161 (entry for 7314).
%H A140078 Seiichi Manyama, <a href="/A140078/b140078.txt">Table of n, a(n) for n = 1..10000</a>
%H A140078 D. A. Goldston, S. W. Graham, J. Pintz and C. Y. Yildirim, <a href="http://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 A140078 {k: k in A033993 and k+1 in A033993}. - _R. J. Mathar_, Jul 19 2023
%t A140078 a = {}; Do[If[Length[FactorInteger[n]] == 4 && Length[FactorInteger[n + 1]] == 4, AppendTo[a, n]], {n, 1, 100000}]; a (* _Artur Jasinski_, May 07 2008 *)
%t A140078 Transpose[Position[Partition[PrimeNu[Range[20000]],2,1],_?(#[[1]] == #[[2]] == 4&),{1},Heads->False]][[1]] (* _Harvey P. Dale_, Jun 21 2013 *)
%t A140078 SequencePosition[PrimeNu[Range[22000]],{4,4}][[;;,1]] (* _Harvey P. Dale_, Jun 20 2024 *)
%o A140078 (PARI) isok(n) = (omega(n)==4) && (omega(n+1)==4); \\ _Michel Marcus_, Sep 04 2015
%Y A140078 Similar sequences with k distinct prime factors: A074851 (k=2), A140077 (k=3), this sequence (k=4), A140079 (k=5).
%Y A140078 Cf. A093548.
%Y A140078 Equals A321504 \ A321494.
%K A140078 nonn
%O A140078 1,1
%A A140078 _Artur Jasinski_, May 07 2008
%E A140078 Link provided by _Harvey P. Dale_, Jun 21 2013

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