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A147525
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Numbers X such that there exists Y in N : X^2 = 309*Y^2 + 103.
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2
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1818362, 233487592671260018, 29981079637522561422843699458, 3849734052023190225799987829591837303402, 494326837141597862882377389715613614004616427568522, 63474260459627156072628000315760330760620752336069144700433378
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OFFSET
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1,1
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COMMENTS
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Obtained with the fundamental unit 64202725495 + 3652365444*sqrt(309) of Q(sqrt(309)).
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LINKS
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FORMULA
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a(n+2) = 128405450990*a(n+1) - a(n).
G.f.: 1818362*x*(1-x)/(1 - 128405450990*x + x^2). - Colin Barker, Oct 21 2014
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EXAMPLE
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a(1)=1818362 because the first relation is : 1818362^2=309*103443^2+103.
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MAPLE
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seq(coeff(series(1818362*x*(1-x)/(1-128405450990*x+x^2), x, n+1), x, n), n = 1..10); # G. C. Greubel, Jan 10 2020
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MATHEMATICA
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LinearRecurrence[{128405450990, -1}, {1818362, 233487592671260018}, 10] (* G. C. Greubel, Jan 10 2020 *)
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PROG
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(PARI) Vec(1818362*x*(1-x)/(1-128405450990*x+x^2) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[1818362, 233487592671260018]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2): n in [1..10]]; # G. C. Greubel, Jan 10 2020
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1818362*x*(1-x)/(1-128405450990*x+x^2) ).list()
(GAP) a:=[1818362, 233487592671260018];; for n in [3..10] do a[n]:=128405450990*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Jan 10 2020
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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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