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

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

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 01 2010

Keywords

• nonn

Comments

The positions of products of 2 successive primes in A001358. - Juri-Stepan Gerasimov, Apr 14 2010

Examples

			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.
		

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.

Crossrefs

Cf. A001358, A006094, A006881.

Programs

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 *)

Formula

a(n) = {k: A001358(k) = A006094(n)}.

Extensions

Entries checked by R. J. Mathar, Feb 09 2010