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A077057
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Minimal (positive) solution a(n) of Diophantine equation a(n)^2 - a(n)*b(n) -G(n)*b(n)^2 = +1 or -1 with G(n) := A078358(n). The companion sequence is b(n)=A077058(n).
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2
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1, 2, 5, 3, 3, 27, 7, 37, 3, 4, 171, 22, 9, 14, 1193, 5, 5, 553, 16, 6173, 11, 45, 143, 849, 6, 6, 18339, 94, 1893, 103, 13, 33, 2001, 115, 12703, 7, 7, 67115, 701, 73, 59, 1891117, 15, 551427, 23, 49771, 39, 4105015, 8, 8, 24673, 41, 75585293, 22, 9095891, 989, 17
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OFFSET
| 1,2
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COMMENTS
| This equation can also be written as (2*a(n)-b(n))^2 - D(n)*b(n)^2 = +4 or -4 with D(n) := A077425(n)=1+4*G(n).
This is from Perron's table (see reference p. 108, for n = 1..28) which gives the minimal x,y values which solve the above mentioned Diophantine equations.
For Pell equation x^2 - D*y^2=+4 see A077428 and A078355. For Pell equation x^2 - D*y^2=-4 see A078356-7.
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REFERENCES
| O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, Satz 3.35, p. 109 and table p. 108).
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FORMULA
| a(n) = (A078361(n) + A077058(n)) / 2 [From Max Alekseyev (maxale(AT)gmail.com), Feb 06 2010]
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CROSSREFS
| Sequence in context: A151960 A115320 A073480 * A030660 A146096 A011310
Adjacent sequences: A077054 A077055 A077056 * A077058 A077059 A077060
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KEYWORD
| nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Feb 06 2010
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