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 A385881 #21 Aug 25 2025 23:34:10 %S A385881 0,0,1,0,0,0,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,2,0,0,1,0,1,0,1,1, %T A385881 1,0,1,1,0,1,1,0,0,2,1,1,0,0,0,0,0,1,2,1,1,2,2,0,2,0,0,0,1,0,1,0,1,1, %U A385881 0,0,1,2,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0,2,0,1,0,1,1,1,0,1,2,1 %N A385881 Algebraic rank of elliptic curve y^2 = x^3 - n*x - n. %C A385881 Terms from n = 43 onward are the analytic ranks (see PARI code) of the corresponding elliptic curves. By the BSD conjecture, these are expected to equal the algebraic ranks. Thus, the validity of these terms is conditional on BSD. %H A385881 LMFDB, <a href="https://www.lmfdb.org/EllipticCurve/Q/368/g/1">y^2 = x^3 - x - 1</a>. %e A385881 a(1) = 0 because y^2 = x^3 - x - 1 has rank 0. %o A385881 (SageMath) %o A385881 for k in range(1, 43): %o A385881 E = EllipticCurve([-k, -k]) %o A385881 print(E.rank(), end=", ") %o A385881 (PARI) a(n) = ellanalyticrank( ellinit([0, 0, 0, -n, -n]) )[1]; \\ _Michel Marcus_, Aug 20 2025 %Y A385881 Cf. A060951, A060952. %K A385881 nonn,new %O A385881 1,26 %A A385881 _Shreyansh Jaiswal_, Aug 20 2025 %E A385881 More terms from _Michel Marcus_, Aug 20 2025