

A176028


The digit leading in the digitsofPi 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 09 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



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

Cf. A099291A099300 (frequency of digits 0..9 in the first 10^n digits of Pi).


KEYWORD

nonn,base


AUTHOR



STATUS

approved



