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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
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.
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
KEYWORD
nonn,more
AUTHOR
Jon E. Schoenfield, Dec 17 2017
EXTENSIONS
a(7)-a(8) from Giovanni Resta, Aug 18 2018
STATUS
approved