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A177760
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Bases m in solutions of the Thue equation s^2 = m^5+z, sorted along increasing z.
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10
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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
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..100.
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FORMULA
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A177761(n)^2 = a(n)^5 + A152412(k) for some k>1.
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EXAMPLE
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(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.
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MATHEMATICA
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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*)
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CROSSREFS
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Cf. A152412, A177761.
Sequence in context: A141483 A230038 A277448 * A329440 A339494 A104731
Adjacent sequences: A177757 A177758 A177759 * A177761 A177762 A177763
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski, May 13 2010
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EXTENSIONS
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Examples and comment on coverage of multiple solutions added - R. J. Mathar, Aug 08 2010
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STATUS
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approved
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