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Search: id:A130647
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| A130647 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+839)^2 = y^2. |
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+0
5
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| 0, 60, 2241, 2517, 2821, 15180, 16780, 18544, 90517, 99841, 110121, 529600, 583944, 643860, 3088761, 3405501, 3754717, 18004644, 19850740, 21886120, 104940781, 115700617, 127563681, 611641720, 674354640, 743497644, 3564911217
(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+839, y).
Corresponding values y of solutions (x, y) are in A159896.
For the generic case x^2+(x+p)^2 = y^2 with p = m^2-2 a (prime) number > 7 in A028871, see A118337.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (843+58*sqrt(2))/839 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (1760979+1141390*sqrt(2))/839^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+1678 for n > 6; a(1)=0, a(2)=60, a(3)=2241, a(4)=2517, a(5)=2821, a(6)=15180.
G.f.: x*(60+2181*x+276*x^2-56*x^3-727*x^4-56*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 839*A001652(k) for k >= 0.
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PROGRAM
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(PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+1678*n+703921), print1(n, ", ")))}
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CROSSREFS
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Cf. A159896, A028871, A118337, A130645, A130646, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159897 (decimal expansion of (843+58*sqrt(2))/839), A159898 (decimal expansion of (1760979+1141390*sqrt(2))/839^2).
Sequence in context: A004364 A054623 A075908 this_sequence A062263 A075917 A058929
Adjacent sequences: A130644 A130645 A130646 this_sequence A130648 A130649 A130650
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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 20 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 30 2009
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