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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, 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
OFFSET
2,7
COMMENTS
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
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 17-28.
LINKS
Steven R. Finch, The Miraculous Bailey-Borwein-Plouffe Pi Algorithm [From the Wayback machine]
Stan Wagon, Is Pi Normal?
Eric Weisstein's World of Mathematics, Normal Number
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
KEYWORD
nonn
AUTHOR
Carl R. White, Jun 26 2002
EXTENSIONS
Edited by Robert G. Wilson v, Jun 27 2002
STATUS
approved