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A114047
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x such that x^2 - 13*y^2 = 1.
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4
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1, 649, 842401, 1093435849, 1419278889601, 1842222905266249, 2391203911756701601, 3103780835237293411849, 4028705132934095091878401, 5229256158767620191964752649, 6787570465375238075075157060001, 8810261234800900253827361899128649
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OFFSET
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0,2
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COMMENTS
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The corresponding values y of the solutions of this Pell equation are given in A075871(n). - Wolfdieter Lang, Jun 27 2013
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LINKS
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FORMULA
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a(0)=1, a(1)=649 then a(n)=1298*a(n-1)-a(n-2). - Benoit Cloitre, Feb 03 2006
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EXAMPLE
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(649^2-1)/13 = 180^2.
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MATHEMATICA
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LinearRecurrence[{1298, -1}, {1, 649}, 20] (* or *) With[{c=180Sqrt[13]}, Simplify[Table[1/2((649-c)^n+(649+c)^n), {n, 0, 20}]]] (* Harvey P. Dale, Aug 11 2011 *)
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PROG
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(PARI) /* This sequence is computed with g(1e9, 13) in the following program. */
g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))
(PARI) a0=1; a1=649; for(n=2, 30, a2=1298*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) \\ Benoit Cloitre
(PARI) Vec((1-649*x)/(1-1298*x+x^2) + O(x^100)) \\ Colin Barker, Jun 13 2015
(Magma) I:=[1, 649]; [n le 2 select I[n] else 1298*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 14 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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