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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
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
Sequence in context: A181522 A031872 A259577 * A254821 A192953 A353232
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 March 29 08:49 EDT 2024. Contains 371268 sequences. (Running on oeis4.)