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a(n) is the smallest positive integer k such that for all x >= k, at least 50% of the integers in the range 1..x contain n in their decimal expansion. In other words, it is the largest integer k such that exactly half of the integers 1..k have n in their decimal expansion.
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%I #16 Sep 12 2021 13:04:53

%S 20327616,1062880,2125762,3188644,4251526,5314408,6377290,17006110,

%T 18068992,19131874

%N a(n) is the smallest positive integer k such that for all x >= k, at least 50% of the integers in the range 1..x contain n in their decimal expansion. In other words, it is the largest integer k such that exactly half of the integers 1..k have n in their decimal expansion.

%C The sequence is inspired by the fact that, for any string of decimal digits, s, "almost all" integers contain s in their decimal expansion. (The same is true for other bases.)

%e a(1) = 1062880 because exactly half of the integers in [1..1062880] have a 1 in their decimal expansion.

%Y Cf. A343839, A344636, A344474.

%Y Also, this sequence has several values that coincide with values in A117862.

%K nonn,more,base

%O 0,1

%A _John Mason_, Jul 29 2021