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 A140078 Numbers k such that k and k+1 have 4 distinct prime factors. 19
 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 The subsequence of terms where k and k+1 are also squarefree is A318896. - R. J. Mathar, Jul 15 2023 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. FORMULA {k: k in A033993 and k+1 in A033993}. - R. J. Mathar, Jul 19 2023 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 *) SequencePosition[PrimeNu[Range[22000]], {4, 4}][[;; , 1]] (* Harvey P. Dale, Jun 20 2024 *) 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 September 14 03:52 EDT 2024. Contains 375911 sequences. (Running on oeis4.)