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 A275108 #30 Apr 25 2020 08:43:29
%S A275108 1,2,3,4,6,10,11,12,16,18,19,22,24,25,26,30,32,34,36,40,42,44,51,56,
%T A275108 64,66,70,71,78,81,85,86,91,106,110,112,128
%N A275108 Record gaps between numbers that are either primes or semiprimes.
%F A275108 a(n) = A275014(n) - A275013(n).
%e A275108 a(5) = 6 because the next prime or semiprime after 241 is 247, and that is a record gap of size 6.
%o A275108 (PARI) checkrange(a, b, r)=while(b-a>r, forstep(n=a+r, a+1, -1, if(bigomega(n)<3, a=n; next(2))); for(n=a+r+1, b, if(bigomega(n)<3, return([a, n])))); 0
%o A275108 print1(1); p=5; r=1; forprime(q=7, 1e9, if(q-p<=r, p=q; next); t=checkrange(p, q, r); while(t, print1(", "t[2]-t[1]); t=checkrange(t[2], q, r=t[2]-t[1])); p=q) \\ _Charles R Greathouse IV_, Nov 19 2016
%Y A275108 Cf. A037143, A111087, A275013, A275014.
%K A275108 nonn,more
%O A275108 1,2
%A A275108 _Bobby Jacobs_, Nov 13 2016
%E A275108 a(32)-a(37) from _Giovanni Resta_, Apr 25 2020