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A074456
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Consider surface area of unit sphere as a function of the dimension d; maximize this as a function of d (considered as a continuous variable); sequence gives decimal expansion of the resulting surface area.
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3
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3, 3, 1, 6, 1, 1, 9, 4, 4, 8, 4, 9, 6, 2, 0, 0, 2, 6, 9, 1, 8, 6, 3, 0, 2, 4, 0, 1, 5, 5, 8, 2, 9, 7, 3, 5, 8, 0, 0, 4, 7, 2, 3, 2, 8, 4, 1, 0, 8, 7, 2, 5, 8, 5, 1, 3, 1, 0, 0, 1, 1, 8, 1, 5, 5, 4, 0, 3, 7, 5, 6, 5, 4, 6, 4, 7, 1, 8, 4, 3, 4, 4, 6, 6, 6, 0, 7, 4, 6, 0, 9, 4, 9, 3, 5, 1, 3, 8, 7
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OFFSET
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2,1
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COMMENTS
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If you set v[n_] := Pi^(n/2)/(n/2)! and s[n_] := n*Pi^(n/2)/(n/2)! and then Plot[{6.283v[n - 2], s[n]}, {n, 0, 20}], the two curves are almost identical.
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LINKS
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EXAMPLE
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33.1611944849620026918630240155829735800472328410872...
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MATHEMATICA
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area[d_] := d * Pi^(d/2)/Gamma[d/2 + 1]; area[x /. FindRoot[PolyGamma[x/2] == Log[Pi], {x, 7}, WorkingPrecision -> 120]] (* Amiram Eldar, Jun 08 2023 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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