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A195835 Leaders in the race of digits of Pi.

%I A195835 #65 Mar 11 2021 21:22:03
%S A195835 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,
%T A195835 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,
%U A195835 4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,1,4
%N A195835 Leaders in the race of digits of Pi.
%C A195835 Next term which is different from earlier in A096567.
%C A195835 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
%C A195835 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
%H A195835 Ruediger Jehn, <a href="/A195835/b195835.txt">Table of n, a(n) for n = 1..3845</a>
%e A195835 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.
%Y A195835 Cf. A000796, A096567, A195844, A195845, A195846, A195847, A342325.
%K A195835 nonn,base
%O A195835 1,1
%A A195835 _Omar E. Pol_, Oct 22 2011
%E A195835 More terms from _D. S. McNeil_, Oct 22 2011