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A098318
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Decimal expansion of [5, 5, ...] = (5 + sqrt(29))/2.
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16
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5, 1, 9, 2, 5, 8, 2, 4, 0, 3, 5, 6, 7, 2, 5, 2, 0, 1, 5, 6, 2, 5, 3, 5, 5, 2, 4, 5, 7, 7, 0, 1, 6, 4, 7, 7, 8, 1, 4, 7, 5, 6, 0, 0, 8, 0, 8, 2, 2, 3, 9, 4, 4, 1, 8, 8, 4, 0, 1, 9, 4, 3, 3, 5, 0, 0, 8, 3, 2, 2, 9, 8, 1, 4, 1, 3, 8, 2, 9, 3, 4, 6, 4, 3, 8, 3, 1, 6, 8, 9, 0, 8, 3, 9, 9, 1, 7, 7, 4, 2, 2, 0
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OFFSET
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1,1
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COMMENTS
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The "metallic" constants A001622, A014176 etc. are defined inserting a = 1, 2, 3, 4, ... into (a+sqrt(a^2+4))/2. [Stakhov & Aranson] - R. J. Mathar, Feb 14 2011
This is the length/width ratio of a 5-extension rectangle; see A188640 where the metallic constants are defined for rational numbers. - Clark Kimberling, Apr 09 2011
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LINKS
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FORMULA
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Equals lim_{n->infinity} S(n, sqrt(29))/ S(n-1, sqrt(29)), with the S-Chebyshev polynomials (see A049310). - Wolfdieter Lang, Nov 15 2023
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EXAMPLE
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5.19258240356725201562535524577016477814756...
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MATHEMATICA
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r=5; 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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(Magma) SetDefaultRealField(RealField(100)); (5 + Sqrt(29))/2; // G. C. Greubel, Jun 30 2019
(Sage) numerical_approx((5+sqrt(29))/2, digits=100) # G. C. Greubel, Jun 30 2019
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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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