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A072136 Position of the first zero in the fractional part of the base n expansion of Pi. +0
1
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)
OFFSET

2,7

COMMENT

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.

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 17-28.

LINKS

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

EXAMPLE

Pi in base 9 is 3.12418812407442... Since the first zero is in the tenth nonary place, a(9)=10.

MATHEMATICA

f[n_] := (rd = RealDigits[Pi, n, 500]; Flatten[ Position[ rd[[1]], 0, 1, 1] - rd[[2]]] [[1]]); Table[ f[n], {n, 2, 75}]

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Carl R.White (cyrek(AT)cyreksoft.yorks.com), Jun 26 2002

EXTENSIONS

Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2002

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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