A358711 - OEIS

%I #47 Jan 25 2023 10:00:05

%S 1210,2020,21200,3211000,42101000,521001000,6210001000,53110100002,

%T 62200010001,541011000021,6401101000310,74011001003100,

%U 840110001031000,9321000001201000,94201000012110000

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

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

%C 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.

%C 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

%H Michael S. Branicky, <a href="/A358711/a358711.py.txt">Python program</a>

%e 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:

%e   Digits(k): 0 1 2 3 4 5 6 7 8 9 10 11 12 (also the Integers(k))

%e   term:      6 4 0 1 1 0 1 0 0 0  3  1  0

%e Note that overlapping integers are counted as well: e.g., 110 is one 11, one 10. 111 is two 11's.

%Y Cf. A046043, A138480, A001477.

%K nonn,base,fini,full

%O 1,1

%A _Marc Morgenegg_, Nov 28 2022

%E a(8) inserted and a(10)-a(15) by _Michael S. Branicky_, Nov 28 2022