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Search: id:A072136
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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
1
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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
(list; graph; listen)
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OFFSET
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2,7
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COMMENT
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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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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 17-28.
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LINKS
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S. R. Finch, The Miraculous Bailey-Borwein-Plouffe Pi Algorithm
Stan Wagon, Is Pi Normal?
Eric Weisstein's World of Mathematics, Link to the 'Normal Number' section of The World of Mathematics
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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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Cf. A000796, A004601, A062964.
Sequence in context: A024426 A034016 A001403 this_sequence A080406 A036682 A104270
Adjacent sequences: A072133 A072134 A072135 this_sequence A072137 A072138 A072139
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KEYWORD
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nonn
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AUTHOR
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Carl R.White (cyrek(AT)cyreksoft.yorks.com), Jun 26 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2002
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