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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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2
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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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The positions of products of 2 successive primes in A001358. - Juri-Stepan Gerasimov, Apr 14 2010
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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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Donovan Johnson, Table of n, a(n) for n = 1..1000
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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a(n) = {k: A001358(k) = A006094(n)}.
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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:
seq(A172348(n), n=1..70) ; # R. J. Mathar, Feb 09 2010
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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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Cf. A001358, A006094, A006881.
Sequence in context: A181522 A031872 A259577 * A254821 A192953 A275970
Adjacent sequences: A172345 A172346 A172347 * A172349 A172350 A172351
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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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Entries checked by R. J. Mathar, Feb 09 2010
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STATUS
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approved
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