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Search: id:A129544
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| A129544 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+137)^2 = y^2. |
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+0
5
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| 0, 115, 136, 411, 1036, 1155, 2740, 6375, 7068, 16303, 37488, 41527, 95352, 218827, 242368, 556083, 1275748, 1412955, 3241420, 7435935, 8235636, 18892711, 43340136, 48001135, 110115120, 252605155, 279771448, 641798283, 1472291068
(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+137, y).
Corresponding values y of solutions (x, y) are in A157213.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (18+5*sqrt(2))/(18-5*sqrt(2)) for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))*(18-5*sqrt(2))^2/(18+5*sqrt(2))^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+274 for n > 6; a(1)=0, a(2)=115, a(3)=136, a(4)=411, a(5)=1036, a(6)=1155.
G.f.: x*(115+21*x+275*x^2-65*x^3-7*x^4-65*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 137*A001652(k) for k >= 0.
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PROGRAM
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(PARI) {forstep(n=0, 1500000000, [3, 1], if(issquare(2*n^2+274*n+18769), print1(n, ", ")))}
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CROSSREFS
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Cf. A157213, A001652, A157214 (decimal expansion of 18+5*sqrt(2)), A157215 (decimal expansion of 18-5*sqrt(2)), A157216 (decimal expansion of (18+5*sqrt(2))/(18-5*sqrt(2))), A129288, A129289, A129298.
Sequence in context: A036269 A036462 A020443 this_sequence A095621 A051975 A122562
Adjacent sequences: A129541 A129542 A129543 this_sequence A129545 A129546 A129547
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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), May 30 2007
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 25 2009
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