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A254937
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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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5
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7, 9, 11, 15, 19, 13, 17, 19, 27, 31, 21, 19, 29, 37, 21, 31, 25, 23, 43, 29, 25, 45, 49, 29, 35, 27, 39, 43, 41, 35, 33, 53, 61, 35, 47, 33, 51, 55, 59, 63, 43, 53, 41, 39, 61, 37, 73, 55, 43
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OFFSET
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1,1
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COMMENTS
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The corresponding positive fundamental solution x2(n) of this second class solutions is given in A254936(n).
See the comments and the Nagell reference in A254934.
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LINKS
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FORMULA
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A254936(n)^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: 11^2 - 2*9^2 = 121 - 162 = -41.
a(2) = -(2*3 - 3*5) = 9.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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