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Search: id:A158484
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| 42, 189, 434, 777, 1218, 1757, 2394, 3129, 3962, 4893, 5922, 7049, 8274, 9597, 11018, 12537, 14154, 15869, 17682, 19593, 21602, 23709, 25914, 28217, 30618, 33117, 35714, 38409, 41202, 44093, 47082, 50169, 53354, 56637, 60018, 63497, 67074
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OFFSET
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1,1
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COMMENT
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If A=[A158484] 49*n.^2-7 (n>0, 42, 189, 434,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X = [A158485] 14*n^2-1 (n>0, 13, 55, 125, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 13^2-42*2^2=1; 55^2-189*4^2=1; 125^2-434*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)=49*n^2-7 (n>0)
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EXAMPLE
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For n=1, a(1)=42; n=2, a(2)=189; n=3, a(3)=434
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CROSSREFS
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Cf. A005843, A158485
Sequence in context: A134385 A115130 A116871 this_sequence A154047 A090198 A008446
Adjacent sequences: A158481 A158482 A158483 this_sequence A158485 A158486 A158487
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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 20 2009
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