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A172348
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Index k of the semiprime A001358(k) = prime(n) * prime(n+1).
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3
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2, 6, 13, 26, 48, 75, 103, 135, 199, 270, 338, 443, 508, 581, 706, 878, 1001, 1124, 1305, 1413, 1565, 1764, 1978, 2299, 2571, 2724, 2886, 3052, 3213, 3710, 4259, 4581, 4859, 5259, 5668, 5954, 6409, 6797, 7184, 7696, 8029, 8515, 9062, 9325, 9608, 10246, 11444
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Band I, B. G. Teubner, Leipzig u. Berlin, 1909.
Derrick H. Lehmer, Guide to Tables in the Theory of Numbers Washington, D.C. 1941.
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LINKS
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E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1 and vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
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FORMULA
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EXAMPLE
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n=1: 6 = 2 * 3 = prime(1) * prime(2) = semiprime(2). Therefore a(1) = 2.
n=2: 15 = 3 * 5 = prime(2) * prime(3) = semiprime(6). Therefore a(2) = 6.
n=3: 35 = 5 * 7 = prime(3) * prime(4) = semiprime(13). Therefore a(3) = 13.
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MAPLE
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A001358 := proc(n) option remember; local a; 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:
A006094 := proc(n) ithprime(n)*ithprime(n+1) ; end proc:
A172348 := proc(n) pp := A006094(n) ; for k from 1 do if A001358(k) = pp then return k; end if; end do ; end proc:
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MATHEMATICA
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semiPrimePi[n_] := Sum[ PrimePi[n/Prime@ i] - i + 1, {i, PrimePi@ Sqrt@ n}]; semiPrimePi@# & /@ Table[ Prime[n] Prime[n + 1], {n, 47}] (* Robert G. Wilson v, Feb 02 2013 *)
nn=50000; Flatten[Module[{sp=Select[Range[nn+PrimePi[nn]], PrimeOmega[#] == 2&]}, Table[ Position[sp, Prime[n]Prime[n+1]], {n, PrimePi[nn]}]]] (* Harvey P. Dale, Sep 07 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 01 2010
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EXTENSIONS
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STATUS
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approved
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