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A114049
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x such that x^2 - 21*y^2 = 1.
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3
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1, 55, 6049, 665335, 73180801, 8049222775, 885341324449, 97379496466615, 10710859270003201, 1178097140203885495, 129579974563157401249, 14252619104807110251895, 1567658521554218970307201
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OFFSET
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0,2
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COMMENTS
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This sequence is computed with g(1e9,21) in the PARI program.
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LINKS
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FORMULA
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a(0)=1, a(1)=55, a(n)=110*a(n-1)-a(n-2). - Benoit Cloitre, Feb 03 2006
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EXAMPLE
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(55^2-1)/21 = 12^2
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MATHEMATICA
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Table[ Numerator@ FromContinuedFraction@ ContinuedFraction[Sqrt@21, Length@ Last@ ContinuedFraction@ Sqrt@21*n], {n, 12}] (* Robert G. Wilson v, Feb 28 2006 *)
LinearRecurrence[{110, -1}, {1, 55}, 20] (* Harvey P. Dale, Jan 27 2013 *)
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PROG
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(PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))
(PARI) a0=1; a1=55; for(n=2, 30, a2=110*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) \\ Benoit Cloitre
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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