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 A103754 #11 May 21 2025 10:40:38 %S A103754 1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1, %T A103754 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2 %N A103754 Number of contiguous digits i in the counting numbers, for i=0. %C A103754 Write the natural numbers as an infinite sequence of digits, starting at the left; and count the digits of each group of "0"'s you encounter (the smallest "groups" have one "0"). %C A103754 From _R. J. Mathar_, May 21 2025: (Start) %C A103754 In the Champernowne constant A033307 zeros appear at places/indices 10, 30, 50, 90, 110, 130,... 170, 190, 191, 193, 196,..., 461, 490, 491, 493, ..., 761, 790, 791, 793, ... 1361, 1390, 1391, 1393,... (This list is related to but not the same as A031299, which uses reversed digits.) %C A103754 Initially the zeros are separated, but occasionally two or more consecutive zeros appear, like (190, 191), (490, 491), (790, 791), obviously triggered by attaching numbers like 100, 200, ...,900, 1000 to the Champernowne constant. %C A103754 In this list of indices are: 10 groups with 1 zero, 1 group with 2 zeros (190,191), 18 groups with 1 zero, 1 group with 2 zeros (490, 491), 18 groups with 1 zero, 1 group with 2 zeros (790, 791) etc; the current sequences writes for each group how many zeros are in it. (End) %Y A103754 Cf. A033307, A103755 (for digit 1), A103756 (for digit 2). %K A103754 base,easy,nonn,less %O A103754 1,11 %A A103754 _Alexandre Wajnberg_, Mar 28 2005