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A222132
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Decimal expansion of sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + ... )))).
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13
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2, 5, 6, 1, 5, 5, 2, 8, 1, 2, 8, 0, 8, 8, 3, 0, 2, 7, 4, 9, 1, 0, 7, 0, 4, 9, 2, 7, 9, 8, 7, 0, 3, 8, 5, 1, 2, 5, 7, 3, 5, 9, 9, 6, 1, 2, 6, 8, 6, 8, 1, 0, 2, 1, 7, 1, 9, 9, 3, 1, 6, 7, 8, 6, 5, 4, 7, 4, 7, 7, 1, 7, 3, 1, 6, 8, 8, 1, 0, 7, 9, 6, 7, 9, 3, 9, 3, 1, 8, 2, 5, 4, 0, 5, 3, 4, 2, 1, 4, 8, 3, 4, 2, 2, 7
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OFFSET
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1,1
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COMMENTS
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Sequence with a(1) = 1 is decimal expansion of sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - ... )))) = A222133.
Because 17 == 1 (mod 4), the basis for integers in the real quadratic number field K(sqrt(17)) is <1, omega(17)>, where omega(17) = (1 + sqrt(17))/2. - Wolfdieter Lang, Feb 10 2020
This is the positive root of the polynomial x^2 - x - 4, with negative root -A222133. - Wolfdieter Lang, Dec 10 2022
It is the spectral radius of the diamond graph (see Seeger and Sossa, 2023). - Stefano Spezia, Sep 19 2023
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LINKS
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FORMULA
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sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + ... )))) - 1 = sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - ... )))). See A222133.
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EXAMPLE
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2.561552812808830274910704...
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MAPLE
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Digits:=140:
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MATHEMATICA
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RealDigits[(1 + Sqrt[17])/2, 10, 130]
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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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