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

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

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

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

Sequence in context: A356096 A326029 A356167 * A375391 A031246 A031245

Adjacent sequences: A176025 A176026 A176027 * A176029 A176030 A176031

Keyword

nonn,base

Author

T. D. Noe, Apr 06 2010

Status

approved