A296653 a(n) is the smallest k > 15 such that the density of semiprimes in 1..k is 1/n.

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.

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