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 A176028 The digit leading in the digits-of-Pi race after n decimal digits. 1

%I #12 Apr 10 2021 22:29:59

%S 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,

%T 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,

%U 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

%N The digit leading in the digits-of-Pi race after n decimal digits.

%C 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?

%H T. D. Noe, <a href="/A176028/b176028.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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}]

%Y Cf. A099291-A099300 (frequency of digits 0..9 in the first 10^n digits of Pi).

%K nonn,base

%O 1,1

%A _T. D. Noe_, Apr 06 2010

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Last modified December 11 09:49 EST 2023. Contains 367722 sequences. (Running on oeis4.)