A358711 Autobiographical numbers: let the k-th digit count the k-th nonnegative integer (A001477(k)) (possibly overlapping) occurrences in the term.

1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000, 53110100002, 62200010001, 541011000021, 6401101000310, 74011001003100, 840110001031000, 9321000001201000, 94201000012110000

Offset

1,1

Comments

The k-th digit must count the k-th nonnegative integer (A001477(k)) appearances in the term.

This sequence is in base b=10. The number of appearances of any integer is always less than b in a term. E.g., the integer '0' can appear at most 9 times in a term.

There are no further terms. This was verified with a computer search of all (permutations of) partitions of d = 1..90 using up to 9 of any digit 0..9 and all (permutations of) "completions" of the remaining d-10 digits consistent with these digit counts. It was verified in each of the two cases for counting appearances: without overlaps (1111 has 2 11's) and with overlaps allowed (1111 has 3 11's). - Michael S. Branicky, Dec 02 2022

Links

Table of n, a(n) for n=1..15.

Michael S. Branicky, Python program

Example

6401101000310 is a term: we have six 0's, four 1's, zero 2's, one 3, one 4, one 6, three 10's and one 11 as integers in the term, visualized as follows:
  Digits(k): 0 1 2 3 4 5 6 7 8 9 10 11 12 (also the Integers(k))
  term:      6 4 0 1 1 0 1 0 0 0  3  1  0
Note that overlapping integers are counted as well: e.g., 110 is one 11, one 10. 111 is two 11's.

Crossrefs

Cf. A046043, A138480, A001477.

Sequence in context: A046043 A358538 A359049 * A138480 A047627 A252213

Adjacent sequences: A358708 A358709 A358710 * A358712 A358713 A358714

Keyword

nonn,base,fini,full

Author

Marc Morgenegg, Nov 28 2022

Extensions

a(8) inserted and a(10)-a(15) by Michael S. Branicky, Nov 28 2022

Status

approved