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 A386407 #20 Aug 03 2025 18:49:00
%S A386407 10658,238337,2628081,17984736,88716544,345948416,1131366096,
%T A386407 3228667360,8266914656,19378404864,42216896176,86468159456,
%U A386407 168013851840,311941643776,556629367184,959168691936,1602434480416,2604149515520,4128340746096,6399632545504
%N A386407 a(n) = -floor(log(Integral_{x=2n^3+2n+2...oo} n^(-x^3) dx)/log(n)).
%C A386407 -a(10) = -2022^3 - 8 was the solution to the final problem of the 2022 MIT Integral Bee Finals; see MIT link.
%H A386407 Jason Bard, <a href="/A386407/b386407.txt">Table of n, a(n) for n = 2..36</a>
%H A386407 MIT, <a href="https://math.mit.edu/~yyao1/pdf/2022_finals.pdf">2022 Integration Bee Finals</a>. See Problem 5.
%H A386407 Prime Newtons, <a href="https://www.youtube.com/watch?v=65kFsIK1oGs">I solved this using Upper Incomplete Gamma</a>, YouTube video.
%F A386407 a(n) = -floor((log(Gamma(1/3, 8 * log(n) * (n^3 + n + 1)^3)) - log(3) - (1/3) * log(log(n))) / log(n)).
%t A386407 Table[-Floor[(Log[Gamma[1/3, 8 (n^3 + n + 1)^3*Log[n]]] - Log[3] - (1/3) Log[Log[n]])/Log[n]], {n, 2, 36}]
%Y A386407 Cf. A071568.
%K A386407 nonn
%O A386407 2,1
%A A386407 _Jason Bard_, Jul 20 2025