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 A180139 #7 Jun 02 2025 03:02:49 %S A180139 4,6,33,36,38,64,66,137,569,5216,367807,939788,6369040,7885439, %T A180139 9536130,140292678,184151167,890838664,912903446,3171881613 %N A180139 a(n)=A179387(n)+1. %C A180139 Theorem (*Artur Jasinski*): %C A180139 For any positive number x >= A180139(n) distance between cube of x and square of any y (such that x<>n^2 and y<>n^3) can't be less than A179386(n+1). %C A180139 Proof: Because number of integral points of each Mordell elliptic curve of the form x^3-y^2 = k is finite and completely computable, such x can't exist. %C A180139 If x=n^2 and y=n^3 distance d=0. %C A180139 For d values see A179386. %C A180139 For y values see A179388. %e A180139 For numbers x from 4 to infinity distance can't be less than 4. %e A180139 For numbers x from 6 to infinity distance can't be less than 7. %e A180139 For numbers x from 33 to infinity distance can't be less than 26. %e A180139 For numbers x from 36 to infinity distance can't be less than 28. %e A180139 For numbers x from 38 to infinity distance can't be less than 49. %e A180139 For numbers x from 66 to infinity distance can't be less than 60. %e A180139 For numbers x from 137 to infinity distance can't be less than 63. %e A180139 For numbers x from 569 to infinity distance can't be less than 174. %e A180139 For numbers x from 5216 to infinity distance can't be less than 207. %e A180139 For numbers x from 367807 to infinity distance can't be less than 307. %Y A180139 Cf. A179107, A179108, A179109, A179387, A179388 %K A180139 hard,more,nonn %O A180139 1,1 %A A180139 _Artur Jasinski_, Aug 12 2010