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Search: id:A158057
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| 17, 33, 49, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 273, 289, 305, 321, 337, 353, 369, 385, 401, 417, 433, 449, 465, 481, 497, 513, 529, 545, 561, 577, 593, 609, 625, 641, 657, 673, 689, 705, 721
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OFFSET
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1,1
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COMMENT
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If A=[A158056] 16*n.^2+2*n (n>0, 18, 68, 150,., ,.,); Y=[A010709] 4 (4,4,4, ,..,); X=[A158057] 16*n+1 (n>0, 17, 33, 49, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 17^2-18*4^2=1; 33^2-68*4^2=1; 49^2-150*4^2=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)=16*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=17; n=2, a(2)=33; n=3, a(3)=49
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CROSSREFS
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Cf. A158056, A010709
A161700, A005408, A016813, A016921, A017281, A017533, A161705, A161709, A161714, A128470. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
Sequence in context: A138393 A044062 A044443 this_sequence A116523 A135637 A040272
Adjacent sequences: A158054 A158055 A158056 this_sequence A158058 A158059 A158060
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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 12 2009
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