A386407 a(n) = -floor(log(Integral_{x=2n^3+2n+2...oo} n^(-x^3) dx)/log(n)).

10658, 238337, 2628081, 17984736, 88716544, 345948416, 1131366096, 3228667360, 8266914656, 19378404864, 42216896176, 86468159456, 168013851840, 311941643776, 556629367184, 959168691936, 1602434480416, 2604149515520, 4128340746096, 6399632545504

Offset: 2

Author

Jason Bard, Jul 20 2025

Keywords

• nonn

Comments

-a(10) = -2022^3 - 8 was the solution to the final problem of the 2022 MIT Integral Bee Finals; see MIT link.

Links

• Jason Bard, Table of n, a(n) for n = 2..36
• MIT, 2022 Integration Bee Finals. See Problem 5.
• Prime Newtons, I solved this using Upper Incomplete Gamma, YouTube video.

Crossrefs

Cf. A071568.

Programs

Mathematica

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}]

Formula

a(n) = -floor((log(Gamma(1/3, 8 * log(n) * (n^3 + n + 1)^3)) - log(3) - (1/3) * log(log(n))) / log(n)).