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Search: id:A158058
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| 14, 60, 138, 248, 390, 564, 770, 1008, 1278, 1580, 1914, 2280, 2678, 3108, 3570, 4064, 4590, 5148, 5738, 6360, 7014, 7700, 8418, 9168, 9950, 10764, 11610, 12488, 13398, 14340, 15314, 16320, 17358, 18428, 19530, 20664, 21830, 23028, 24258, 25520
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OFFSET
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1,1
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COMMENT
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If A=[A158058] 16*n.^2-2*n (n>0, 14, 60, 138,., ,.,); Y=[A010709] 4 (4,4,4, ,..,); X=[A125169] 16*n+115 (15, 31, 47, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 15^2-14*4^2=1; 31^2-60*4^2=1; 47^2-138*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^2-2*n (n>0)
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EXAMPLE
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For n=1, a(1)=14; n=2, a(2)=60; n=3, a(3)=138
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CROSSREFS
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Cf. A010709, A125169
Sequence in context: A100174 A120371 A062022 this_sequence A100171 A063492 A051799
Adjacent sequences: A158055 A158056 A158057 this_sequence A158059 A158060 A158061
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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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