A103754 Number of contiguous digits i in the counting numbers, for i=0.

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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2

Offset

1,11

Comments

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)

Links

Table of n, a(n) for n=1..49.

Crossrefs

Cf. A033307, A103755 (for digit 1), A103756 (for digit 2).

Sequence in context: A374326 A318829 A113515 * A375668 A058665 A327103

Adjacent sequences: A103751 A103752 A103753 * A103755 A103756 A103757

Keyword

base,easy,nonn,less

Author

Alexandre Wajnberg, Mar 28 2005

Status

approved