A177760 - OEIS

A177760

Bases m in solutions of the Thue equation s^2 = m^5+z, sorted along increasing z.

1, 2, 1, 5, 3, 1, 2, 1, 23, 2, 1, 27, 3, 1, 2, 1, 4, 2, 1, 3, 2, 7, 1, 2, 3, 1, 5, 4, 2, 1, 6, 3, 2, 1, 12, 2, 1, 3, 4, 1, 2, 5, 3, 1, 2, 4, 3, 1, 2, 1, 6, 2, 3, 21, 4, 7, 5, 8, 1, 2, 73, 3, 1, 2, 4, 3, 26, 1, 2, 5, 1, 3, 9, 10, 2, 4, 6, 20, 1, 3, 2, 11, 1, 4, 2, 5, 3, 7, 1, 2, 3, 4, 1, 6, 29, 2, 3, 5, 8, 1

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OFFSET

1,2

COMMENTS

The equation has solutions for the positive z listed in A152412.

A177761 and this sequence here show pairs (s,m) that solve given these z>0. (The case z=0 has infinitely many solutions which are not included here.)

There is no 1-to-1 relation to these z because more than one (s,m) may exist for some z, in case of which all are listed here.

LINKS

Table of n, a(n) for n=1..100.

FORMULA

A177761(n)^2 = a(n)^5 + A152412(k) for some k>1.

EXAMPLE

(s=59, m=5=a(57), z=356) and (s=182, m=8=a(58), z=356) are solutions associated with z = A152412(57) =356.

(s=20, m=2=a(60), z=368) and (s=45531, m=73=a(61), z=368) are solutions associated with z = A152412(59) =368.

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}]; bb (*Artur Jasinski*)

CROSSREFS

Cf. A152412, A177761.

Sequence in context: A141483 A230038 A277448 * A329440 A339494 A104731

Adjacent sequences: A177757 A177758 A177759 * A177761 A177762 A177763

KEYWORD

nonn

AUTHOR

Artur Jasinski, May 13 2010

EXTENSIONS

Examples and comment on coverage of multiple solutions added - R. J. Mathar, Aug 08 2010

STATUS

approved