A359049 Autobiographical numbers k whose decimal digits are a concatenation count(0), count(1), ..., count(m) for some m, where count(j) is the number of (possibly overlapping) occurrences of j within the digits of k itself.

1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000, 53110100002, 62200010001, 541011000021, 6401101000310, 74011001003100, 840110001031000, 1040110000031000, 9321000001201000, 94201000012110000, 1160010100041000010, 11611001000320000100, 13313000000001200000, 13313000000100200000

Offset

1,1

Comments

In other words: Counting the zeros (j=0) in the term gives the first concatenation of decimal digits (number of zeros) in the term, counting all ones, gives the second, and so on.

A term can have any number of digits.

This sequence is in base 10.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..30

Michael S. Branicky, Python Program

Example

1040110000031000 is a term: we have ten 0's, four 1's, zero 2's, one 3, one 4, three 10's and one 11 as integers in the term, visualized as follows:
  Integers(j): 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
  term:       10 4 0 1 1 0 0 0 0 0  3  1  0  0  0
Notice that overlapping integers are counted so 110 is one 11, one 10 (or 111 would be two 11's).

Crossrefs

Cf. A046043, A138480.

Sequence in context: A135239 A046043 A358538 * A358711 A138480 A047627

Adjacent sequences: A359046 A359047 A359048 * A359050 A359051 A359052

Keyword

nonn,base

Author

Marc Morgenegg, Dec 14 2022

Extensions

a(17)-a(20) from Michael S. Branicky, Dec 14 2022

Status

approved