OFFSET
1,1
COMMENTS
This is the sequence of the k-th prime for k = {4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,...}. Not to be confused with A106350: semiprimes indexed by primes.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Paul Kinlaw, Megan Triplett, and William Tripp, Almost Primes of Almost Prime Index, INTEGERS, Vol 24 (2024), Article #A99.
FORMULA
a(n) = prime(semiprime(n)).
pi(a(n)) = p*q for some primes p and q.
Sum_{n>=1} 1/a(n) is in the interval (0.9910, 0.9915) (Kinlaw et al., 2024, Theorem 6, p. 11). - Amiram Eldar, Nov 09 2024
EXAMPLE
a(1) = 7 because semiprime(1) = 4, so prime(semiprime(1)) = prime(4) = 7.
MATHEMATICA
Prime@ Select[Range@ 161, PrimeOmega@ # == 2 &] (* or *) Select[Prime@ Range@ 161, PrimeOmega@ PrimePi@ # == 2 &] (* Michael De Vlieger, Nov 28 2015 *)
PROG
(Magma) [NthPrime(n): n in [2..200] | &+[d[2]: d in Factorization(n)] eq 2]; // Vincenzo Librandi, Nov 28 2015
(PARI) lista(nn) = select(x->(bigomega(primepi(x))==2), primes(nn)); \\ Michel Marcus, Nov 29 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Apr 29 2005
STATUS
approved