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Search: id:A031689
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| A031689 |
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Least term in period of continued fraction for sqrt(n) is 11. |
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5
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| 123, 488, 1095, 1944, 3035, 4368, 5943, 7760, 9819, 12120, 14663, 16152, 17448, 19344, 20475, 23744, 27255, 31008, 35003, 37284, 39240, 43719, 48440, 53403, 53866, 58608, 59093, 64055, 64562, 67128, 69744, 75675, 81848, 88263, 94920, 101819
(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=[A031689] 121*n.^2+2*n (n>0) (123,488,1095,..,); Y=[A157613] 2662*n+22 (2684, 5346, 8008..,); X=[A157614] 29282*n^2+484*n+1 (29767, 118097, 264991,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 29767^2-123*2684^2=1; 118097^2-488*5346^2=1; 264991^2-1095*8008^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009]
If A=[A031689] 121*n.^2+2*n (n>0, 123, 488, 1095,.,. ,.,); Y=[A010850] 11 (11, 11, 11,.,); X=[A158131] 121*n+1 (n>0, 122, 243, 364, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 122^2-123*11^2=1; 243^2-488*11^2=1; 364^2-1095*11^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
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LINKS
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Wolfram MathWorld, Pell Equation [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009]
Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009]
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FORMULA
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a(n)=121*n^2+2*n (n>0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009]
a(n)=121*n^2+2*n (n>0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
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EXAMPLE
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For n=1, a(1)=123; n=2, a(2)=488; n=3, a(3)=1095 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
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CROSSREFS
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Cf. A157613, A157614 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009]
Cf. A010850. A158131 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
Adjacent sequences: A031686 A031687 A031688 this_sequence A031690 A031691 A031692
Sequence in context: A004945 A004965 A091331 this_sequence A074303 A077379 A135475
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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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