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 A205300 #36 May 12 2025 14:01:43
%S A205300 6,14,4,119,933,21161,588821,26600591
%N A205300 Least semiprime for which n-1 iterations of "Look & Say" (A045918) all yield semiprimes, but not the n-th iteration.
%C A205300 a(8) > 10^7. - _Tyler Busby_, Feb 07 2023
%C A205300 a(9) > 10^8. - _Daniel Suteu_, Feb 08 2023
%e A205300 All of the following are the least semiprime with the required characteristics.
%e A205300 a(1) = 6 because 6 is a semiprime and its 'Look & Say' transformation A045918(6) = 16 is not a semiprime. (The smaller semiprime 4 yields LS(4)=14 which is again a semiprime.)
%e A205300 a(2) = 14 because both 14 and A045918(14)=1114 are semiprimes but LS(1114)=3114 is not.
%e A205300 a(3) = 4 because 4 (2*2), 14 (2*7) and 1114 (2*557) are all semiprimes but 3114 (2*3*3*173) is not.
%t A205300 LookAndSayA[n_] := FromDigits@ Flatten@ IntegerDigits@ Flatten[ Through[ {Length, First}[#]] & /@ Split@ IntegerDigits@ n]; semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Block[{k = 1, truth = Append[Table[True, {n}], False]}, While[ semiPrimeQ@# & /@ NestList[ LookAndSayA, k, n] != truth, k++]; k]
%o A205300 (PARI) A205300(n) = for(a=4,1e9,bigomega(a)==2||next; my(t=a); for(k=2,n, bigomega(t=A045918(t))!=2 && next(2)); bigomega(A045918(t))==2 || return(a)) \\ _M. F. Hasler_, Jan 30 2012
%Y A205300 Cf. A001358, A056815, A204541.
%K A205300 nonn,base,hard,more
%O A205300 1,1
%A A205300 _Robert G. Wilson v_, Jan 27 2012
%E A205300 a(7) from _Tyler Busby_, Feb 07 2023
%E A205300 a(8) from _Daniel Suteu_, Feb 08 2023
%E A205300 a(5) corrected by _Giovanni Resta_, May 12 2025