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A176028
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The digit leading in the digits-of-Pi race after n decimal digits.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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?
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A099291-A099300 (frequency of digits 0..9 in the first 10^n digits of Pi).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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