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 A379449 #14 Jan 07 2025 08:40:22 %S A379449 3,4,5,8,13,19,24,29,34,45,47,51,56,61,71,107,127,140,184,192,198,274, %T A379449 284,375,384,559,592,630,689,774,792,834,1133,1213,1241,1315,1947 %N A379449 Numbers k such that the prime gap between the consecutive primes p1 < k! = factorial(k) < p2 sets a new record. %e A379449 a(1) = 3, because the prime gap between the consecutive primes 5 < 3! < 7 sets the first record of 2. %e A379449 n gap p1 < x! < p2 %e A379449 1 2 5 < 3! < 7; %e A379449 2 6 23 < 4! < 29; %e A379449 3 14 113 < 5! < 127; %e A379449 4 54 40289 < 8! < 40343; %e A379449 5 90 6227020777 < 13! < 6227020867; %e A379449 6 190 121645100408831899 < 19! < 121645100408832089; %e A379449 7 204 620448401733239439359927 < 24! < 620448401733239439360131; %Y A379449 Cf. A054588, A350100, A378429. %K A379449 nonn,more %O A379449 1,1 %A A379449 _Jean-Marc Rebert_, Dec 23 2024 %E A379449 a(37) from _Jinyuan Wang_, Dec 23 2024