A106130 -id:A106130 - cp's OEIS frontend

A357023 Semiprimes k such that k is congruent to 5 modulo k's index in the sequence of semiprimes.

4, 185, 206, 209, 27681, 3066905, 3067135, 3067795, 3067985, 348933197, 348933239, 348933251, 348933257, 348933269, 44690978141, 44690978162, 44690978519, 44690978561, 44690978617, 44690978869, 44690978981, 44690979457, 44690979527, 6553736049293

Offset: 1

Lucas A. Brown, Oct 14 2022

a(32) > 8040423200947.

			The 1st semiprime is 4, which is congruent to 5 (mod 1), so 4 is in the sequence.
The 2nd semiprime is 6, which is not congruent to 5 (mod 6), so 6 is not in the sequence.
The 60th semiprime is 185, which is congruent to 5 (mod 60), so 185 is in the sequence.

Lucas A. Brown, Table of n, a(n) for n = 1..31
Lucas A. Brown, semiprimemods.py.

Cf. A001358, A106130.

a(n) = A001358(A106130(n)).

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

Original entry on oeis.org

18, 26432, 3066830, 348933114, 44690978122, 6553736049264

Offset: 3

Jon E. Schoenfield, Dec 17 2017

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.

			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.

Cf. A001358, A066265, A106130.

a(n) = exp(n log n + n log log n + O(n)). - Charles R Greathouse IV, Dec 14 2022

a(7)-a(8) from Giovanni Resta, Aug 18 2018

cp's OEIS Frontend

A357023 Semiprimes k such that k is congruent to 5 modulo k's index in the sequence of semiprimes.

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