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A176439
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Decimal expansion of (7+sqrt(53))/2.
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9
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7, 1, 4, 0, 0, 5, 4, 9, 4, 4, 6, 4, 0, 2, 5, 9, 1, 3, 5, 5, 4, 8, 6, 5, 1, 2, 4, 5, 7, 6, 3, 5, 1, 6, 3, 9, 6, 8, 8, 8, 8, 3, 4, 8, 4, 1, 2, 8, 8, 2, 3, 8, 7, 1, 9, 1, 8, 9, 0, 9, 0, 8, 9, 5, 6, 4, 2, 0, 5, 7, 8, 6, 9, 3, 1, 2, 4, 5, 2, 5, 9, 1, 6, 6, 4, 7, 8, 9, 7, 0, 4, 5, 4, 0, 4, 6, 3, 3, 7, 6, 0, 9, 6, 3, 1
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OFFSET
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1,1
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COMMENTS
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Continued fraction expansion of (7+sqrt(53))/2 is A010727.
This is the shape of a 7-extension rectangle; see A188640 for definitions. [From Clark Kimberling, Apr 09 2011]
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LINKS
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FORMULA
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Equals lim_{n->oo} S(n, sqrt(53))/S(n-1, sqrt(53)), with the S-Chebyshev polynomials (see A049310). - Wolfdieter Lang, Nov 15 2023
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EXAMPLE
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(7+sqrt(53))/2 = 7.14005494464025913554...
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MATHEMATICA
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r=7; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
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PROG
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CROSSREFS
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Cf. A010506 (decimal expansion of sqrt(53)), A010727 (all 7's sequence).
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KEYWORD
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AUTHOR
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STATUS
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approved
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