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 A140078 Numbers k such that k and k+1 have 4 distinct prime factors. 14
 7314, 8294, 8645, 9009, 10659, 11570, 11780, 11934, 13299, 13629, 13845, 14420, 15105, 15554, 16554, 16835, 17204, 17390, 17654, 17765, 18095, 18290, 18444, 18920, 19005, 19019, 19095, 19227, 20349, 20405, 20769, 21164, 21489, 21735 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite. - Charles R Greathouse IV, Jun 02 2016 REFERENCES David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 161 (entry for 7314). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 D. A. Goldston, S. W. Graham, J. Pintz and C. Y. Yildirim., Small gaps between almost primes, the parity problem and some conjectures of Erdos on consecutive integers, arXiv:0803.2636 [math.NT], 2008. MATHEMATICA a = {}; Do[If[Length[FactorInteger[n]] == 4 && Length[FactorInteger[n + 1]] == 4, AppendTo[a, n]], {n, 1, 100000}]; a (* Artur Jasinski, May 07 2008 *) Transpose[Position[Partition[PrimeNu[Range[20000]], 2, 1], _?(#[[1]] == #[[2]] == 4&), {1}, Heads->False]][[1]] (* Harvey P. Dale, Jun 21 2013 *) PROG (PARI) isok(n) = (omega(n)==4) && (omega(n+1)==4); \\ Michel Marcus, Sep 04 2015 CROSSREFS Similar sequences with k distinct prime factors: A074851 (k=2), A140077 (k=3), this sequence (k=4), A140079 (k=5). Cf. A093548. Equals A321504 \ A321494. Sequence in context: A206080 A253939 A116248 * A321504 A318896 A328786 Adjacent sequences:  A140075 A140076 A140077 * A140079 A140080 A140081 KEYWORD nonn AUTHOR Artur Jasinski, May 07 2008 EXTENSIONS Link provided by Harvey P. Dale, Jun 21 2013 STATUS approved

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Last modified June 4 05:19 EDT 2020. Contains 334815 sequences. (Running on oeis4.)