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A072136
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Position of the first zero in the fractional part of the base n expansion of Pi.
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0
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1, 1, 1, 1, 1, 1, 3, 10, 32, 5, 5, 5, 19, 16, 13, 19, 7, 25, 25, 15, 9, 17, 29, 23, 60, 35, 3, 6, 4, 91, 20, 30, 51, 85, 70, 103, 33, 44, 28, 3, 52, 17, 60, 62, 9, 187, 4, 39, 39, 10, 13, 8, 37, 14, 56, 18, 20, 142, 4, 38, 57, 131, 17, 14, 33, 101, 40, 6, 42, 15, 68, 191, 149, 24
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OFFSET
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2,7
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COMMENTS
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The first digit after the decimal point is indexed 1.
Given that in a normal number there is a 1/n possibility that each basimal place is a zero and that Pi is held to be normal in all integer bases, the statistically expected value of a(n) is n.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 17-28.
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LINKS
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EXAMPLE
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Pi in base 9 is 3.12418812407442... Since the first zero is in the tenth nonary place, a(9)=10.
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MATHEMATICA
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f[n_] := (rd = RealDigits[Pi, n, 500]; Flatten[ Position[ rd[[1]], 0, 1, 1] - rd[[2]]] [[1]]); Table[ f[n], {n, 2, 75}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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