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 A296653 a(n) is the smallest k > 15 such that the density of semiprimes in 1..k is 1/n. 0
 18, 26432, 3066830, 348933114, 44690978122, 6553736049264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS The condition that k > 15 is included in the definition because the ratio (number of semiprimes in 1..k)/k is 0 for k < 4 and reaches its maximum value (2/5) only at k = 10 (the 4th semiprime) and at k = 15 (the 6th semiprime), and decreases (although not monotonically) beyond that. LINKS Table of n, a(n) for n=3..8. FORMULA a(n) = exp(n log n + n log log n + O(n)). - Charles R Greathouse IV, Dec 14 2022 EXAMPLE For k > 15, the ratio (number of semiprimes in 1..k)/k first decreases to -- 1/3 at k = 18 (the 6th semiprime), so a(3) = 18; 1/4 at k = 26432 (the 6608th semiprime), so a(4) = 26432. CROSSREFS Cf. A001358, A066265, A106130. Sequence in context: A129042 A262359 A202155 * A255406 A123401 A201494 Adjacent sequences: A296650 A296651 A296652 * A296654 A296655 A296656 KEYWORD nonn,more AUTHOR Jon E. Schoenfield, Dec 17 2017 EXTENSIONS a(7)-a(8) from Giovanni Resta, Aug 18 2018 STATUS approved

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Last modified November 30 23:40 EST 2023. Contains 367464 sequences. (Running on oeis4.)