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A172348 Index k of the semiprime A001358(k) = prime(n) * prime(n+1). 2
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 A275970

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 July 14 15:44 EDT 2020. Contains 335729 sequences. (Running on oeis4.)