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 A114412 Records in semiprime gaps ordered by merit. 16
 2, 3, 4, 6, 11, 19, 24, 28, 30, 32, 38, 47, 54, 70, 74, 107, 110, 112, 120, 126, 146 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There is an associated index list n = 1, 2, 4, 6, 34, 422, 1765, 4585, 8112, 8650, 8861, 75150, ... and an associated semiprime list A001358(n) = 4, 6, 10, 15, 1418, 6559, 17965, 32777, 35103, 35981, 340894, ... - R. J. Mathar, Mar 15 2009 LINKS Eric Weisstein's World of Mathematics, Semiprime. Eric Weisstein's World of Mathematics, Prime Gaps. FORMULA a(n) = records in A065516/log(A001358(n)) = records in (A001358(n+1) - A001358(n))/log(A001358(n))). EXAMPLE Records defined in terms of A065516 and A001358: .   n  A065516(n)  A065516(n)/log_10(A001358(n))   =  ==========  ==============================   1       2      2 / log_10(4)  = 3.32192809...   2       3      3 / log_10(6)  = 3.85529162...   3       1      1 / log_10(9)  = 1.04795163...   4       4      4 / log_10(10) = 4.00000000   5       1      1 / log_10(14) = 0.87250286...   6       6      6 / log_10(15) = 5.10164492...   7       1      1 / log_10(21) = 0.75630419...   8       3      3 / log_10(22) = 2.23476557...   9       1      1 / log_10(25) = 0.71533827... MATHEMATICA sp = 4; m0 = 0;  l = {}; lim = 1000000; For[i = 5, i <= lim, i++, If[PrimeOmega[i] == 2, m = (i - sp)/Log[sp]; If[m > m0, m0 = m; AppendTo[l, i - sp]]; sp = i] ]; l (* Robert Price, Oct 29 2018 *) CROSSREFS Cf. A001358, A065516, A111870, A111871, A113688-A113693, A114403-A114411, A114412-A114422. Sequence in context: A111124 A295681 A117308 * A016038 A003099 A061941 Adjacent sequences:  A114409 A114410 A114411 * A114413 A114414 A114415 KEYWORD nonn,more AUTHOR Jonathan Vos Post, Nov 25 2005 EXTENSIONS Corrected and extended by Charles R Greathouse IV, Oct 05 2006 a(16)-a(21) from Donovan Johnson, Feb 17 2010 STATUS approved

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Last modified March 23 02:53 EDT 2019. Contains 321422 sequences. (Running on oeis4.)