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A243903 Numbers n such that (number of primes <= n) is greater than or equal to (number of semiprimes <= n). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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).
LINKS
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]]]
CROSSREFS
Sequence in context: A348553 A032521 A246102 * A296867 A228144 A236841
KEYWORD
nonn
AUTHOR
Harvey P. Dale, Jun 14 2014
STATUS
approved

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Last modified June 16 14:12 EDT 2024. Contains 373430 sequences. (Running on oeis4.)