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%I #12 Jul 10 2021 20:35:56
%S 11824560,14283650,14283666,14283672,14422716,14872610,14872612,
%T 14881986,14917048,22453380,29875904,29877516,29878760,29878776,
%U 29878782,29878812,29879052,29880432,31852820,31852822,31888098,31894108,31894110,31894130,32255514,32527482,32557320,32565868,32565888,32565890,32566068,32568748,32568822,32569040,33082200
%N The complete list of numbers k such that precisely half of the numbers from 1 to k contain consecutive repeated digits.
%C Consider a function f(n), which looks at all of the numbers from 1 to n, counts up how many contain consecutive repeated digits, and how many do not, and subtracts the former count from the latter count. For all numbers less than 11824560, f(n) is positive; for all numbers greater than 33082200, f(n) is negative. In between, the function crosses the zero line several times, with the 35 numbers in this sequence being the only values for which f(n)=0.
%e Among the 29878776 numbers up to and including 29878776, 14939388 contain at least one pair of consecutive digits that are identical, and 14939388 contain no such pair.
%e Of the six numbers that follow 29878776, 3 have consecutive repeated digits and 3 do not, so therefore 29878782 is also in this list.
%K nonn,base,fini,full
%O 1,1
%A _Elliott Line_, Jan 11 2017
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