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Search: id:A158462
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| 30, 138, 318, 570, 894, 1290, 1758, 2298, 2910, 3594, 4350, 5178, 6078, 7050, 8094, 9210, 10398, 11658, 12990, 14394, 15870, 17418, 19038, 20730, 22494, 24330, 26238, 28218, 30270, 32394, 34590, 36858, 39198, 41610, 44094, 46650, 49278, 51978
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OFFSET
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1,1
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COMMENT
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If A=[A158462] 36*n.^2-6 (n>0, 30, 138, 318,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X = [A158463] 12*n^2-1 (n>0, 11, 47, 107, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 11^2-30*2^2=1; 47^2-138*4^2=1; 107^2-318*6^2=1.
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LINKS
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
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FORMULA
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a(n)=36*n^2-6 (n>0)
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EXAMPLE
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For n=1, a(1)=30; n=2, a(2)=138; n=3, a(3)=318
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CROSSREFS
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Cf. A005843, A158463
Sequence in context: A100147 A079588 A117750 this_sequence A064495 A124958 A126417
Adjacent sequences: A158459 A158460 A158461 this_sequence A158463 A158464 A158465
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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 19 2009
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