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A263008
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First member T0(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, 1, 1, 3, 1, 13, 1, 1, 5, 7, 1, 1, 3, 59, 1, 1, 7, 23, 1, 221, 7, 1, 1, 1, 9, 3, 7, 11, 1, 1, 47, 5, 31, 15, 1, 1, 11, 193, 3, 103, 3, 1, 8807, 1, 3383, 3, 21, 3, 8005, 1, 1, 13, 17, 3, 2047
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OFFSET
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1,4
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COMMENTS
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The 2-happy numbers D(n)*E(n) are given in A007970(n) (called rhombic numbers in the Conway paper). D(n) = A191856(n), E(n) = A191857(n). Here the corresponding smallest positive numbers satisfying E(n)*U(n)^2 - D(n)*T(n)^2 = +2, n >= 1, with odd U(n) and T(n) are given as T0(n) = a(n) and U0(n) = A263009(n).
In the W. Lang link the first U0(n) and T0(n) numbers are given in the Table for d(n) = A007970(n), n >= 1.
In the Zumkeller link "Initial Happy Factorization Data" given in A191860 the a(n) = T0(n) numbers appear for the t = 2 rows in column v.
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LINKS
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FORMULA
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EXAMPLE
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n = 6: 2-happy number A007970(6) = 19 = 1*19 = A191856(6)*A191857(6). 19*A263009(6)^2 - 1*a(6)^2 = 19*3^2 - 1*13^2 = +2. This is the smallest positive solution for the given 2-happy couple (A191856(n), A191857(n)).
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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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