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Search: id:A031702
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| A031702 |
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Numbers n such that least term in period of continued fraction for sqrt(n) is 24. |
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7
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| 145, 578, 1299, 2308, 3605, 5190, 7063, 9224, 11673, 14410, 17435, 20748, 24349, 28238, 32415, 36880, 41633, 46674, 52003, 57620, 63525, 69718, 76199, 82968, 90025, 97370, 97994, 105003, 112924, 121133, 129630, 138415, 147488, 156849, 166498
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If A=[A156711] 144*n^2+127*n+28 (28,299,858,..,], or A=[A156719] 144*n^2-127*n+28 (28,45,350,...,), or A=[A156635] 144*n^2-n (143,574,1293), or A=[A031702] (145,578,1299,..., except the term 97994); Y=[A010863] (24,24,24,...,); X=[A156702] (127,161,287,..,) then we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 127^2-28*24^2=1; 161^2-45*24^2=1; 287^2-143*24^2=1; 289^2-145*24^2=1; 415^2-299*24^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 21 2009]
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LINKS
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Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 21 2009]
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EXAMPLE
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The continued fraction of sqrt(97994) is 313, [25, 24, 25, 626], where the smallest element of the period is 24, so 97994 belongs in the sequence.
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CROSSREFS
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Cf. A156711, A156719, A156635, A010863, A156702 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 21 2009]
Sequence in context: A158133 A094613 A116208 this_sequence A031600 A008377 A076464
Adjacent sequences: A031699 A031700 A031701 this_sequence A031703 A031704 A031705
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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