A177761 Values s on hyperelliptic curves s^2=m^5+z sorted along increasing z.

2, 6, 3, 56, 16, 4, 7, 5, 2537, 8, 6, 3788, 17, 7, 9, 8, 33, 10, 9, 18, 11, 130, 10, 12, 19, 11, 57, 34, 13, 12, 89, 20, 14, 13, 499, 15, 14, 21, 35, 15, 16, 58, 22, 16, 17, 36, 23, 17, 18, 18, 90, 19, 24, 2021, 37, 131, 59, 182, 19, 20, 45531, 25, 20, 21, 38, 26, 3447, 21, 22

Offset

1,1

Links

Table of n, a(n) for n=1..69.

Formula

a(n)^2 = A177760(n)^5 + A152412(k) for some k.

Mathematica

aa = {}; bb = {}; cc = {}; Do[Do[If[(N[Sqrt[x^5 + n], 300] - Round[Sqrt[x^5 + n]])^2 < 10^-300, AppendTo[aa, n]; AppendTo[bb, x]; AppendTo[cc, Round[Sqrt[x^5 + n]]] , {x, 1, 100}], {n, 1, 100000}]; cc (*Artur Jasinski*)

Crossrefs

Cf. A177760, A152412

Sequence in context: A111678 A206429 A101819 * A128192 A354375 A077750

Adjacent sequences: A177758 A177759 A177760 * A177762 A177763 A177764

Keyword

nonn

Author

Artur Jasinski, May 13 2010

Status

approved