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 A177760 Bases m in solutions of the Thue equation s^2 = m^5+z, sorted along increasing z. 10
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 23 10:10 EDT 2023. Contains 361443 sequences. (Running on oeis4.)