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 A286894 #37 Feb 16 2025 08:33:45
%S A286894 0,1,2,4,6,6,14,14,14,20,34,34,34,44,72,72,72,86,114,114,148,148,154,
%T A286894 154,210,220,222,248,282,282,292,336,354,382,456,464,468,486,532,540,
%U A286894 602,652,674,716,766,778,804,906,906,906
%N A286894 a(n) = maximum difference between two consecutive primes up to 2^n.
%H A286894 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PrimeGaps.html">Prime Gaps</a>
%e A286894 Up to 2^5 = 32, the maximum difference between two consecutive primes is 6 (at 29 - 23), so a(5)=6.
%t A286894 a[n_] := If[n == 1, 0, Prime[Range[PrimePi[NextPrime[2^n, -1]]]] // Differences // Max]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 30}]
%o A286894 (PARI) a(n) = {maxg = 0; p = 2; forprime(q=3, 2^n, maxg = max(maxg, q-p); p=q;); maxg;} \\ _Michel Marcus_, May 15 2017
%Y A286894 Cf. A038460, A053303.
%K A286894 nonn,more
%O A286894 1,3
%A A286894 _Jean-François Alcover_, May 15 2017
%E A286894 a(33)-a(50) from _David A. Corneth_, May 16 2017