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A158936
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List of coprime pairs (x,y) such that x^2+y^2=13^n with 0<x<y.
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4
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0, 1, 2, 3, 5, 12, 9, 46, 119, 120, 122, 597, 828, 2035, 4449, 6554, 239, 28560, 56403, 86158, 145668, 341525, 246046, 1315911, 3369960, 3455641, 3627003, 17021162, 23161315, 58317492, 128629846, 186118929, 13651680, 815616479, 1590277918, 2474152797, 4241902555, 9719139348, 6712571031, 37641223154, 95420159401, 99498527400, 107655263398, 485257533003
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For n>2, all other solutions (x,y) are divisible by 13, e.g., 26^2+39^2=13^3.
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FORMULA
| n=1: 13^1=2^2+3^2, hence a(1)=2, a(2)=3,
n=2: 13^2=5^2+12^2, hence a(3)=5, a(4)=12.
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MATHEMATICA
| s={2, 3}; x=2; y=3; Do[A=3x+2y; If[Mod[A, 13]==0, A=Abs[3x-2y]; B=2x+3y, B=Abs[2x-3y]]; x=A; If[A>B, x=B; y=A, y=B]; s=Join[s, {x, y}], {20}]; s
Table[Select[PowersRepresentations[13^n, 2, 2], CoprimeQ @@ # &][[1]], {n, 0, 21}] (* T. D. Noe, Apr 12 2011 *)
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CROSSREFS
| Cf. A098122 for case x^2+y^2=5^n.
Cf. A188948, A188949 for the values of x and y separately.
Cf. A188982, A188983 for even and odd terms.
Sequence in context: A162253 A112978 A187129 * A002139 A140489 A193776
Adjacent sequences: A158933 A158934 A158935 * A158937 A158938 A158939
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KEYWORD
| nonn,tabf
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Apr 10 2011
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