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 A105999 #21 Sep 01 2024 20:36:42
%S A105999 1,4,10,26,77,235,779,2785,10643,43697,192893,915218,4657929,25380749,
%T A105999 147721169,916036271,6037442989,42191467826,311911160465,
%U A105999 2434014941905,20007995450483,172911791611798,1568190042677867
%N A105999 Semiprimeth recurrence: a(0) = 1, a(n+1) = semiprime(a(n)) = A001358(a(n)).
%C A105999 Semiprime equivalent of R. G. Wilson's primeth recurrence: A007097.
%e A105999 a(1) = A001358(1) = 4,
%e A105999 a(2) = A001358(a(1)) = A001358(4) = 10,
%e A105999 a(3) = A001358(a(2)) = A001358(10) = 26.
%t A105999 SemiPrimePi[n_] := Sum[PrimePi[n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; NestList[SemiPrime@# &, 1, 18] (* _Robert G. Wilson v_, May 31 2006 *)
%Y A105999 Cf. A001358, A007097, A091022, A105997, A105998.
%K A105999 nonn
%O A105999 0,2
%A A105999 _Jonathan Vos Post_, Apr 29 2005
%E A105999 a(5)-a(15) from _Robert G. Wilson v_, Apr 30 2005
%E A105999 a(16)-a(20) from _Robert G. Wilson v_, May 31 2006
%E A105999 a(21)-a(22) from _Donovan Johnson_, Sep 24 2010