A243903 Numbers n such that (number of primes <= n) is greater than or equal to (number of semiprimes <= n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 31, 32, 33

Offset: 1

Author

Harvey P. Dale, Jun 14 2014

Keywords

• nonn

Comments

Conjecture: there are no additional terms.

We know from the asymptotic formulas (see Landau) that the sequence is finite. See also the graph of A243906. - N. J. A. Sloane, Jun 14 2014

References

• E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1, Teubner, Leipzig, 1909; third edition : Chelsea, New York (1974).

Crossrefs

Cf. A000040, A000720, A001358, A072000, A243906.

Programs

Mathematica

With[{nn=5000},Flatten[Position[Thread[{Accumulate[Table[ If[ PrimeOmega[n] == 2,1,0],{n,nn}]],PrimePi[Range[nn]]}],_?(Last[#]>=First[#]&),{1}, Heads-> False]]]