cp's OEIS Frontend

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").

From R. J. Mathar, May 21 2025: (Start)

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.)

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.

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)