

A358711


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


1



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

1,1


COMMENTS

The kth digit must count the kth 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 d10 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



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



KEYWORD

nonn,base,fini,full


AUTHOR



EXTENSIONS



STATUS

approved



