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A176028 The digit leading in the digits-of-pi race after n decimal digits. 1
3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

That is, we count the frequency of each of the ten digits 0-9 in the first n digits of pi and set a(n)=d, where d is the digit with the highest frequency. If there is a tie, we take the least digit. Surprisingly, in the first 10^8 digits, the digit 6 never has the lead, the digit 0 has the lead only 516 times, and the digit 4 has the lead over 71% of the time. Is this the behavior of a normal number?

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

EXAMPLE

The first 20 digits of pi are 3.1415926535897932384. After the initial 3, it is clear that 1 has the lead until the 11th digit, when the third 5 occurs.

MATHEMATICA

nn=1000; cnt=Table[0, {10}]; d=RealDigits[Pi, 10, nn+1][[1]]; Table[cnt[[1+d[[n]]]]++; mx=Max[cnt]; Position[cnt, mx, 1, 1][[1, 1]]-1, {n, nn}]

CROSSREFS

A099291-A099300 (frequency of 10^n digits of pi)

Sequence in context: A030557 A086997 A074298 * A031246 A031245 A031244

Adjacent sequences:  A176025 A176026 A176027 * A176029 A176030 A176031

KEYWORD

nonn,base

AUTHOR

T. D. Noe, Apr 06 2010

STATUS

approved

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Last modified December 8 11:15 EST 2016. Contains 278939 sequences.