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Search: id:A130005
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| A130005 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+577)^2 = y^2. |
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+0
5
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| 0, 35, 1568, 1731, 1908, 10595, 11540, 12567, 63156, 68663, 74648, 369495, 401592, 436475, 2154968, 2342043, 2545356, 12561467, 13651820, 14836815, 73214988, 79570031, 86476688, 426729615, 463769520, 504024467, 2487163856, 2703048243
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also values x of Pythagorean triples (x, x+577, y).
Corresponding values y of solutions (x, y) are in A159626.
For the generic case x^2+(x+p)^2 = y^2 with p = 2*m^2-1 a (prime) number in A066436 see A118673 or A129836.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (579+34*sqrt(2))/577 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (855171+556990*sqrt(2))/577^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+1154 for n > 6; a(1)=0, a(2)=35, a(3)=1568, a(4)=1731, a(5)=1908, a(6)=10595.
G.f.: x*(35+1533*x+163*x^2-33*x^3-511*x^4-33*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 577*A001652(k) for k >= 0.
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PROGRAM
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(PARI) {forstep(n=0, 500000000, [3, 1], if(issquare(2*n^2+1154*n+332929), print1(n, ", ")))}
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CROSSREFS
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Cf. A159626, A066436, A118673, A118674, A129836, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159627 (decimal expansion of (579+34*sqrt(2))/577), A159628 (decimal expansion of (855171+556990*sqrt(2))/577^2).
Sequence in context: A158733 A029560 A135923 this_sequence A001825 A094187 A115963
Adjacent sequences: A130002 A130003 A130004 this_sequence A130006 A130007 A130008
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KEYWORD
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nonn
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AUTHOR
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Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 15 2007
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EXTENSIONS
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Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 21 2009
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