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A106350
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Semiprimes indexed by primes.
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16
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6, 9, 14, 21, 33, 35, 49, 55, 65, 86, 91, 115, 122, 129, 142, 159, 183, 187, 206, 215, 218, 247, 259, 287, 303, 319, 323, 334, 339, 358, 403, 415, 446, 451, 482, 489, 511, 527, 537, 553, 573, 581, 626, 633, 655, 667, 698, 737, 753, 758, 771, 791, 794, 835, 851
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OFFSET
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1,1
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COMMENTS
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This is the sequence of the n-th semiprime for n = {2,3,5,7,11,13,17,19,23,29...}. Not to be confused with A106349: Primes indexed by semiprimes. We seek to know what this sequence is asymptotically, as J. B. Rosser's result, subsequently modified, is that prime(n) ~ n*(log n + log log n - 1). hence semiprime(prime(n)) ~ semiprime(n)*(log semiprime(n) + log log semiprime(n) - 1). But what is, asymptotically, semiprime(n)?
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LINKS
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FORMULA
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EXAMPLE
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a(1) = semiprime(prime(1)) = semiprime(2) = 6.
a(2) = semiprime(prime(2)) = semiprime(3) = 9.
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MAPLE
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A001358 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 then return a ; end if; end do ; end if ; end proc: A106350 := proc(n) A001358(ithprime(n)) ; end proc: seq(A106350(n), n=1..80) ; # R. J. Mathar, Dec 14 2009
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MATHEMATICA
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terms = 55;
semiPrimes = Select[Range[16 terms], PrimeOmega[#] == 2&];
(* NB If the index Prime[terms] exceeds the size of the table semiPrimes, then the coefficient 16 has to be increased according to the number of terms desired: for instance, for 1000 terms, replace 16 with 32. *)
a[n_] := semiPrimes[[Prime[n]]];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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All values after a(32) corrected by R. J. Mathar, Dec 14 2009
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STATUS
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approved
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