A072136 Position of the first zero in the fractional part of the base n expansion of Pi.

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

Table of n, a(n) for n=2..75.

Steven R. Finch, The Miraculous Bailey-Borwein-Plouffe Pi Algorithm [Broken link]

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

Cf. A000796, A004601, A062964.

Sequence in context: A325579 A034016 A001403 * A286444 A080406 A036682

Adjacent sequences: A072133 A072134 A072135 * A072137 A072138 A072139

Keyword

nonn

Author

Carl R. White, Jun 26 2002

Extensions

Edited by Robert G. Wilson v, Jun 27 2002

Status

approved