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 A172348 Index k of the semiprime A001358(k) = prime(n) * prime(n+1). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The positions of products of 2 successive primes in A001358. - Juri-Stepan Gerasimov, Apr 14 2010 REFERENCES 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. LINKS 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. FORMULA a(n) = {k: A001358(k) = A006094(n)}. EXAMPLE 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. MAPLE 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 MATHEMATICA 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 *) CROSSREFS Cf. A001358, A006094, A006881. Sequence in context: A181522 A031872 A259577 * A254821 A192953 A353232 Adjacent sequences: A172345 A172346 A172347 * A172349 A172350 A172351 KEYWORD nonn AUTHOR Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 01 2010 EXTENSIONS Entries checked by R. J. Mathar, Feb 09 2010 STATUS approved

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)