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A031645
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Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 57.
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0
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40049, 40853, 66130, 67162, 67681, 98717, 188581, 235514, 237458, 238433, 298477, 300665, 365257, 370105, 436129, 440098, 442754, 508994, 510421, 513281, 514714, 516149, 521909, 523354, 524801, 593629, 686425, 703085, 785957, 796625
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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cf57Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[s][[2]]]; len= Length[cf]; OddQ[len]&&cf[[(len-1)/2]]==cf[[(len+1)/2]]==57]; Select[Range[800000], cf57Q] (* Harvey P. Dale, Jan 17 2024 *)
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CROSSREFS
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KEYWORD
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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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