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Search: id:A122694
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| A122694 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+761)^2 = y^2. |
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+0
4
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| 0, 583, 820, 2283, 5440, 6783, 15220, 33579, 41400, 90559, 197556, 243139, 529656, 1153279, 1418956, 3088899, 6723640, 8272119, 18005260, 39190083, 48215280, 104944183, 228418380, 281021083, 611661360, 1331321719, 1637912740
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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+761, y).
Corresponding values y of solutions (x, y) are in A160200.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (1003+462*sqrt(2))/761 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (591603+85478*sqrt(2))/761^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+1522 for n > 6; a(1)=0, a(2)=583, a(3)=820, a(4)=2283, a(5)=5440, a(6)=6783.
G.f.: x*(583+237*x+1463*x^2-341*x^3-79*x^4-341*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 761*A001652(k) for k >= 0.
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PROGRAM
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(PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1522*n+579121), print1(n, ", ")))}
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CROSSREFS
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Cf. A160200, A001652, A115135, A156035 (decimal expansion of 3+2*sqrt(2)), A160201 (decimal expansion of (1003+462*sqrt(2))/761), A160202 (decimal expansion of (591603+85478*sqrt(2))/761^2).
Sequence in context: A127694 A162705 A059468 this_sequence A032373 A037995 A043428
Adjacent sequences: A122691 A122692 A122693 this_sequence A122695 A122696 A122697
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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 03 2007
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EXTENSIONS
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Edited and one term added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 18 2009
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