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A263009
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Second member U0(n) of the smallest positive pair (T0(n), U0(n)) for the n-th 2-happy number couple (D(n), E(n)).
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3
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1, 3, 1, 1, 1, 3, 5, 1, 1, 39, 3, 1, 1, 9, 7, 1, 1, 3, 1, 27, 59, 3, 9, 1, 1, 1, 3, 15, 5, 1, 477, 1, 3, 7, 11, 1, 1, 2175, 17, 9, 7, 3, 747, 1, 41571, 1, 5, 19, 627, 13, 1, 1, 9, 5, 153
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OFFSET
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1,2
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COMMENTS
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See A263008. E(n)*a(n)^2 - D(n)*A263008(n)^2 = +2, n >= 1, with the 2-happy couple (D(n), E(n)) = (A191856(n), A191857(n)). The 2-happy numbers D(n)*E(n) are given by A007970(n).
In the Zumkeller link "Initial Happy Factorization Data" given in A191860 the a(n) = U0(n) numbers appear for the t = 2 rows in column w.
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LINKS
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FORMULA
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EXAMPLE
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n = 4: 2-happy number A007970(4) = 11 = 1*11 =
A191856(4)*A191857(4). 11*a(4)^2 - 1*A263008(4)^2 = 11*1^2 - 1*3^2 = +2. This is the smallest positive solution for given (D, E) = (1, 11).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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