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 A283267 #26 Mar 06 2017 03:48:14
%S A283267 2,3,4,4,6,6,3,7,7,3,7,7,3,4,4,4,4,5,5,5,3,4,11,11,11,5,5,4,6,4,7,7,9,
%T A283267 9,3,5,3,8,5,5,7,7,7,7,4,5,9,9,9,10,10,4,5,3,7,7,4,9,9,4,4,5,5,5,5,4,
%U A283267 9,9,9,3,6,6,4,4,5,3,5,4,5,5,10,10,8,8,4
%N A283267 Smallest b-a such that a < prime(n) < b, where a,b are semiprimes.
%C A283267 This is the first sequence from the series of sequences: "Smallest b-a such that a < prime(n)^k < b, where a,b are semiprimes", k = 1, 2, 3, ... .
%C A283267 This series of sequences was inspired by _Zak Seidov_'s message to Seqfans (Mar 02 2017) where he suggested listing the triples of primes squared with neighbor semiprimes.
%C A283267 There are no semiprimes below prime(2) = 3 but there are below prime(3) = 5 so the offset is 3. - _David A. Corneth_, Mar 04 2017
%C A283267 From _Michael De Vlieger_, Mar 04 2017: (Start)
%C A283267 Largest term in range a(3)..a(10^m): {7, 11, 24, 38, 54, 74, ...}.
%C A283267 Largest term in range a(3)..a(2^m), m>1: {3, 6, 7, 11, 11, 14, 19, 20, 24, 25, 38, 38, 38, 47, 47, 55, 70, 74, ...}.
%C A283267 Largest run in range a(3)..a(10^m): {2, 4, 6, 8, 10, 12, ...}.
%C A283267 Largest run in range a(3)..a(2^m), m>1: {1, 2, 2, 4, 4, 4, 4, 5, 6, 7, 7, 8, 8, 10, 10, 10, 12, 12, ...}. (End)
%H A283267 Charles R Greathouse IV, <a href="/A283267/b283267.txt">Table of n, a(n) for n = 3..10000</a>
%F A283267 a(n) = A102414(n) - A102415(n). - _Michel Marcus_, Mar 04 2017
%e A283267 For a(3), the largest semiprime below 5 is 4. The least semiprime above 5 is 6. Therefore, (a, b) = (4, 6) giving a(3) = 6 - 4 = 2. - _David A. Corneth_, Mar 04 2017
%t A283267 Table[Module[{p = Prime@ n, a, b}, a = p - 1; b = p + 1; While[PrimeOmega@ a != 2, a--]; While[PrimeOmega@ b != 2, b++]; b - a], {n, 3, 120}] (* _Michael De Vlieger_, Mar 04 2017 *)
%o A283267 (PARI) issemi(n)=bigomega(n)==2
%o A283267 a(n,p=prime(n))=my(a=p,b=p); while(!issemi(a--), ); while(!issemi(b++), ); b-a \\ _Charles R Greathouse IV_, Mar 04 2017
%Y A283267 Cf. A000040, A001358, A037143.
%K A283267 nonn
%O A283267 3,1
%A A283267 _Vladimir Shevelev_, Mar 04 2017
%E A283267 More terms from _Peter J. C. Moses_, Mar 04 2017