# [seqfan] Re: Sequence A031702

David Wilson davidwwilson at comcast.net
Sun Feb 15 11:44:58 CET 2009

```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.

97994 looks out of place because most of the small elements of A031702 are
of the form 144 k^2 + k, where sqrt(144 k^2 + k) has the continued fraction
12k, [24, 24k]. 97994 is the first element that breaks this pattern.

----- Original Message -----
From: <vincenzo.librandi at tin.it>
To: <seqfan at seqfan.eu>
Sent: Sunday, February 15, 2009 3:29 AM
Subject: [seqfan] Sequence A031702

>I believe that the number 97994 is not in sequence A031702.
>
> Regards,
> Vincenzo Librandi
>
> %I A031702
> %S A031702
> 145,578,1299,2308,3605,5190,7063,9224,11673,14410,17435,20748,24349,
> %T
> A031702
> 28238,32415,36880,41633,46674,52003,57620,63525,69718,76199,82968,90025,
> %U A031702
> 97370,97994,105003,112924,121133,129630,138415,147488,156849,166498
> %N
> A031702 Least term in period of continued fraction for sqrt(n) is 24.
> %
> Y A031702 Sequence in context: A051414 A094613 A116208 this_sequence
> A031600 A008377
>               A076464
> A031699 A031700 A031701 this_sequence A031703 A031704
>
> A031705
> %K A031702 nonn
> %O A031702 1,1
> %A A031702 David W. Wilson
> (davidwwilson(AT)comcast.net)
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

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