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A254763
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One half of the fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = A007519(n), n>=1 (primes congruent to 1 mod 8).
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8
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2, 4, 6, 5, 4, 8, 7, 9, 7, 6, 11, 14, 9, 7, 16, 11, 15, 18, 8, 14, 20, 10, 9, 19, 15, 22, 14, 13, 16, 20, 23, 13, 11, 25, 17, 28, 16, 15, 14, 13, 23, 18, 26, 29, 16, 32, 13, 20, 28, 24
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OFFSET
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1,1
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COMMENTS
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The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A254762(n).
See the comments and the Nagell reference in A254760.
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LINKS
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FORMULA
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A254762(n)^2 - 2*(2*a(n))^2 = A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
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EXAMPLE
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n = 2: 13^2 - 2*(2*4)^2 = 169 - 128 = 41.
The smallest positive solution is (x1(2), y1(2)) = (7, 2) from (A254760(2), 2*A254761(2)).
a(4) = 11 - 3*2 = 5.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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