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A338284
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a(n) is the smallest nonsquare m such that the second partial quotient in the continued fraction for sqrt(m) equals n.
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1
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7, 2, 23, 5, 47, 10, 79, 17, 119, 26, 167, 37, 223, 50, 287, 65, 359, 82, 439, 101, 527, 122, 623, 145, 727, 170, 839, 197, 959, 226, 1087, 257, 1223, 290, 1367, 325, 1519, 362, 1679, 401, 1847, 442, 2023, 485, 2207, 530, 2399, 577, 2599, 626, 2807, 677, 3023, 730
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OFFSET
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1,1
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LINKS
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FORMULA
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For odd n, a(n) = A073577((n+1)/2) = n^2 + 4*n + 2.
O.g.f.: (7 + 2*x + 2*x^2 - x^3 - x^4 + x^5) / ((1-x)^3 * (1+x)^3).
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EXAMPLE
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a(3) = 23, since sqrt(23) = [4; 1, 3, ...] and m=23 is the smallest integer such that sqrt(m) has with second partial quotient equal 3.
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MATHEMATICA
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CoefficientList[Series[(7 + 2*x + 2*x^2 - x^3 - x^4 + x^5) / ((1-x)^3 * (1+x)^3), {x, 0, 20}], x] (* Georg Fischer, Aug 18 2021 *)
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CROSSREFS
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Cf. A013945 (first partial quotient = n).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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