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A332133
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Decimal expansion of (1 + sqrt(3))/2, unique positive root of x^2 - x - 1/2.
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2
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1, 3, 6, 6, 0, 2, 5, 4, 0, 3, 7, 8, 4, 4, 3, 8, 6, 4, 6, 7, 6, 3, 7, 2, 3, 1, 7, 0, 7, 5, 2, 9, 3, 6, 1, 8, 3, 4, 7, 1, 4, 0, 2, 6, 2, 6, 9, 0, 5, 1, 9, 0, 3, 1, 4, 0, 2, 7, 9, 0, 3, 4, 8, 9, 7, 2, 5, 9, 6, 6, 5, 0, 8, 4, 5, 4, 4, 0, 0, 0, 1, 8, 5, 4, 0, 5, 7, 3, 0, 9, 3, 3, 7, 8, 6, 2, 4, 2, 8, 7, 8, 3, 7, 8
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OFFSET
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1,2
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COMMENTS
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Also, max {a, b} where {a,b} is the unique solution of a + b = 1 and a^2 + b^2 = 2 (implying also ab = -1/2 and a^3 + b^3 = 5/2 without solving for a, b). See A332122 for a generalization to 3 variables {a, b, c}.
This is a non-integer element of the quadratic number field Q(sqrt(3)) with the given monic minimal polynomial. The other negative root is -(-1 + sqrt(3))/2 = - A152422. - Wolfdieter Lang, Aug 30 2022
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LINKS
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EXAMPLE
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1.3660254037844386467637231707529361834714026269051903140279...
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MATHEMATICA
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RealDigits[(1 + Sqrt[3])/2, 10, 120][[1]] (* Amiram Eldar, Jun 21 2023 *)
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PROG
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(PARI) localprec(111); digits(solve(a=0, 2, a^2-a-1/2)\.1^99)
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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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