This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355328 #26 Jul 07 2022 02:01:00
%S A355328 1,0,0,1,1,0,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,
%T A355328 0,0,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,
%U A355328 0,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1
%N A355328 Decimal expansion of the number whose binary expansion differs from its decimal expansion only in the first digit.
%C A355328 The decimal fraction 0.1 has binary expansion starting with 0.0001...; copying the suffix 001 (3 digits, as 3 < log_2(10) < 4) we obtain 0.1001, which expands to 0.00011001101, etc.
%C A355328 Alternatively the process can be described as greedily expressing 1/2 with digits of weights 1/2^n-1/10^n. With f(n)=1/2^n-1/10^n, 0.5 = f(1)+f(4)+f(5)+f(8)+f(9)+f(11)...
%e A355328 0.100110011010000011001111010001110100101001000111010001001101001011...
%t A355328 seq[len_] := Module[{s = Table[0, {len}], x = 1/10, n = 1, c = 0}, s[[1]] = 1; While[n < len, While[1/2^n - 1/10^n > x, n++]; c++; s[[n]] = 1; x -= (1/2^n - 1/10^n)]; s]; seq[100] (* _Amiram Eldar_, Jun 29 2022 *)
%Y A355328 Cf. A352677 (golden base = binary).
%K A355328 nonn,cons
%O A355328 0,1
%A A355328 _Leonid Broukhis_, Jun 29 2022