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A067872
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Least m > 0 for which m*n^2 + 1 is a square.
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6
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3, 2, 7, 3, 23, 8, 47, 15, 79, 24, 119, 2, 167, 48, 3, 63, 287, 80, 359, 6, 88, 120, 527, 28, 623, 168, 727, 12, 839, 44, 959, 255, 216, 288, 8, 20, 1367, 360, 19, 77, 1679, 22, 1847, 30, 208, 528, 2207, 7, 2399, 624, 128, 42, 2807, 728, 696, 3, 160, 840, 3479, 11
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OFFSET
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1,1
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COMMENTS
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Least m > 0 for which x^2 - m*y^2 = 1 has a solution with y = n.
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LINKS
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FORMULA
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For n a power of an odd prime, a(n) = n^2 - 2. For n twice a power of an odd prime, a(n) = (n/2)^2 - 1. - T. D. Noe, Sep 13 2007
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EXAMPLE
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a(4)=3, based on 3*4^2 + 1 = 7^2.
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MATHEMATICA
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a[n_] := For[m=1, True, m++, If[IntegerQ[Sqrt[m*n^2+1]], Return[m]]]; Table[a[n], {n, 100}]
lm[n_]:=Module[{m=1}, While[!IntegerQ[Sqrt[m n^2+1]], m++]; m]; Array[lm, 60] (* Harvey P. Dale, Feb 24 2013 *)
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PROG
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(Haskell)
a067872 n = (until ((== 1) . a010052 . (+ 1)) (+ nn) nn) `div` nn
where nn = n ^ 2
(Python)
y, x, n2 = n*(n+2), 2*n+3, n**2
m, r = divmod(y, n2)
while r:
y += x
x += 2
m, r = divmod(y, n2)
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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