This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A106349 #18 Nov 09 2024 04:38:49
%S A106349 7,13,23,29,43,47,73,79,97,101,137,139,149,163,167,199,227,233,257,
%T A106349 269,271,293,313,347,373,389,421,439,443,449,467,487,491,499,577,607,
%U A106349 631,647,653,661,673,677,727,751,757,811,821,823,829,839,907,929,937,947
%N A106349 Primes indexed by semiprimes.
%C A106349 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.
%H A106349 Michael De Vlieger, <a href="/A106349/b106349.txt">Table of n, a(n) for n = 1..10000</a>
%H A106349 Paul Kinlaw, Megan Triplett, and William Tripp, <a href="https://math.colgate.edu/~integers/y99/y99.pdf">Almost Primes of Almost Prime Index</a>, INTEGERS, Vol 24 (2024), Article #A99.
%F A106349 a(n) = prime(semiprime(n)).
%F A106349 a(n) = A000040(A001358(n)).
%F A106349 pi(a(n)) = p*q for some primes p and q.
%F A106349 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
%e A106349 a(1) = 7 because semiprime(1) = 4, so prime(semiprime(1)) = prime(4) = 7.
%t A106349 Prime@ Select[Range@ 161, PrimeOmega@ # == 2 &] (* or *) Select[Prime@ Range@ 161, PrimeOmega@ PrimePi@ # == 2 &] (* _Michael De Vlieger_, Nov 28 2015 *)
%o A106349 (Magma) [NthPrime(n): n in [2..200] | &+[d[2]: d in Factorization(n)] eq 2]; // _Vincenzo Librandi_, Nov 28 2015
%o A106349 (PARI) lista(nn) = select(x->(bigomega(primepi(x))==2), primes(nn)); \\ _Michel Marcus_, Nov 29 2015
%Y A106349 Cf. A000040, A000720, A001358, A007097, A091022, A105997, A105998, A106350.
%K A106349 nonn,easy
%O A106349 1,1
%A A106349 _Jonathan Vos Post_, Apr 29 2005