A309142 Rank of elliptic curve y^2 = x^3 + (n^2 - 6*n -3)*x^2 + 16*n*x.

0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1

Offset

10,65

Comments

a(n) is undefined for n = 0, 1 or 9.

Links

Jinyuan Wang, Table of n, a(n) for n = 10..5000

Andrew Bremner, Richard K. Guy, Richard J. Nowakowski, Which integers are representable as the product of the sum of three integers with the sum of their reciprocals?, Math. Comp. 61 (1993), 117-130.

Allan J. MacLeod, Knight's Problem

Prog

(PARI) {a(n) = ellanalyticrank(ellinit([0, n^2-6*n-3, 0, 16*n, 0]))[1]}

Crossrefs

Cf. A085514, A086446, A309143, A309144, A309146.

Sequence in context: A316868 A106822 A203905 * A064532 A321922 A362496

Adjacent sequences: A309139 A309140 A309141 * A309143 A309144 A309145

Keyword

nonn

Author

Seiichi Manyama, Jul 14 2019

Status

approved