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Search: id:A089223
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| A089223 |
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Product of a dimensional spectrum in primes to natural integers. |
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+0
1
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| 1, 2, 3, 4, 6, 10, 14, 20, 29, 42, 62, 90, 128, 182, 261, 376, 535, 764, 1087, 1532, 2166, 3052, 4311, 6128, 8680, 12207, 17118, 23849, 33148, 46761, 65779, 92558, 129518, 182289, 255222, 357379, 500442, 699118, 976654, 1364261, 1897468, 2649692
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A infinite Root Polynomial of the form: P(x)=Product[(x-Log[Prime[n+1]]/Log[n+1]),{n,1,Infinity}] would be important in dimensional theory of self-similar fractals and useful in generalized sets like Sierpinski sets and von Koch sets as conversion of fractal dimension to nearest topological dimension.
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FORMULA
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a(n) = Floor[Product[Log(Prime[i+1]]/Log[i+1], {i, 1, n}]]
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MATHEMATICA
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f[n_]=Log[Prime[n+1]]/Log[n+1] g[n_]=Product[f[i], {i, 1, n}] digits=100 a=Table[Floor[g[n]], {n, 1, digits}]
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CROSSREFS
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Sequence in context: A061018 A130126 A121152 this_sequence A094861 A097699 A086990
Adjacent sequences: A089220 A089221 A089222 this_sequence A089224 A089225 A089226
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 10 2003
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