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 A166237 Differences between consecutive products of two distinct primes: a(n) = A006881(n+1) - A006881(n). 12
 4, 4, 1, 6, 1, 4, 7, 1, 1, 3, 1, 7, 5, 4, 2, 1, 4, 3, 4, 5, 3, 5, 3, 1, 1, 4, 2, 1, 1, 11, 5, 4, 3, 1, 3, 1, 6, 4, 1, 7, 1, 1, 2, 1, 9, 3, 1, 2, 5, 11, 1, 5, 2, 2, 7, 7, 1, 1, 2, 1, 3, 4, 1, 1, 2, 1, 1, 2, 5, 9, 2, 10, 2, 4, 1, 5, 3, 3, 2, 7, 4, 9, 4, 4, 3, 1, 2, 1, 1, 2, 4, 5, 5, 2, 2, 3, 1, 2, 5, 1, 4, 2, 5, 9, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Goldston, Graham, Pintz & Yıldırım (2005) prove that a(n+1) - a(n) <= 26 infinitely often. They improve this constant to 6 in their 2009 paper. - Charles R Greathouse IV, Dec 26 2020 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 D. A. Goldston, S. W. Graham, J. Pintz and C. Y. Yıldırım, Small gaps between primes and almost primes, arXiv:math/0506067 [math.NT], 2005; Proceedings of the London Mathematical Society 98:3 (May 2009), pp. 741-774. Yang Liu, Peter S. Park, and Zhuo Qun Song, Bounded gaps between products of distinct primes, arXiv:1607.03887 [math.NT], 2016-2017; Research in Number Theory 3:26 (2017). Keiju Sono, Small gaps between the set of products of at most two primes, arXiv:1605.02920 [math.NT], 2016-2018; Journal of the Mathematical Society of Japan 72:1 (2020), pp. 81-118. MATHEMATICA f[n_]:=Last/@FactorInteger[n]=={1, 1}; a=6; lst={}; Do[If[f[n], AppendTo[lst, n-a]; a=n], {n, 9, 6!}]; lst PROG (PARI) {m=106; v=vector(m); n=0; c=0; while(c

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Last modified November 30 19:14 EST 2022. Contains 358453 sequences. (Running on oeis4.)