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A195835
Leaders in the race of digits of Pi.
8
3, 1, 5, 3, 9, 8, 2, 8, 4, 8, 2, 8, 2, 4, 1, 9, 1, 9, 1, 9, 1, 9, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 1, 4
OFFSET
1,1
COMMENTS
Next term which is different from earlier in A096567.
The number 4 wins 71.7% of the first 100 million races (occurs most often in 71.7% of the races). It is also the leader after 100 million digits with a comfortable lead (10,003,863 occurrences compared to 10,002,475 occurrences of the 1 that was winning 15.9% of the first 100 million races). All numbers except the 6 were in the lead at some time. Number 6 was almost in the lead after 48,500 digits, only two occurrences short of the 1 at that time. In the first 100,000,000 digits of Pi the number 6 appears about 4450 times less than the current leader 4. But as the next comment shows the 6 finally takes the lead after 990,213,634 digits. - Ruediger Jehn, Jan 27 2021
Position at which a number (0 to 9) is leader for the first time: 174999, 4, 187, 1, 274, 11, 990213634, 320741, 108, 59 (see A342325). - Kester Habermann, Jan 27 2021
LINKS
EXAMPLE
The decimal expansion of Pi = 3.1415926535... starts with 3 (see A000796) hence the first leader in the race of digits is 3, so a(1) = 3. After 4 stages the new leader is 1 because the number 1 appears twice and the earlier leader appears once, so a(2) = 1. After 11 stages the new leader is 5 because the number 5 appears three times and the earlier leader appears twice, so a(3) = 5.
KEYWORD
nonn,base
AUTHOR
Omar E. Pol, Oct 22 2011
EXTENSIONS
More terms from D. S. McNeil, Oct 22 2011
STATUS
approved