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Search: id:A157888
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| 90, 333, 738, 1305, 2034, 2925, 3978, 5193, 6570, 8109, 9810, 11673, 13698, 15885, 18234, 20745, 23418, 26253, 29250, 32409, 35730, 39213, 42858, 46665, 50634, 54765, 59058, 63513, 68130, 72909, 77850, 82953, 88218, 93645, 99234, 104985
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OFFSET
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1,1
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COMMENT
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If A=[A157888] 81*n.^2+9 (90,333,738,.,); Y=[A005843] 2*n (n>0, 2,4,6,8,.,); X=[A157889] 18*n^2+1 (19, 73, 163,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 19^2-90 *2^2=1; 73^2-333*4^2=1; 163^2-738*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=81*n^2+9 (n>0)
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EXAMPLE
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For n=1, a(1)=90; n=2, a(2)=333; n=3, a(3)=738
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CROSSREFS
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Cf. A005843, A157889
Sequence in context: A044803 A074213 A027621 this_sequence A158490 A066116 A156738
Adjacent sequences: A157885 A157886 A157887 this_sequence A157889 A157890 A157891
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009
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