cp's OEIS Frontend

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.

%I A359049 #32 Jan 12 2023 18:44:10
%S A359049 1210,2020,21200,3211000,42101000,521001000,6210001000,53110100002,
%T A359049 62200010001,541011000021,6401101000310,74011001003100,
%U A359049 840110001031000,1040110000031000,9321000001201000,94201000012110000,1160010100041000010,11611001000320000100,13313000000001200000,13313000000100200000
%N 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.
%C A359049 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.
%C A359049 A term can have any number of digits.
%C A359049 This sequence is in base 10.
%H A359049 Michael S. Branicky, <a href="/A359049/b359049.txt">Table of n, a(n) for n = 1..30</a>
%H A359049 Michael S. Branicky, <a href="/A359049/a359049.txt">Python Program</a>
%e A359049 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:
%e A359049   Integers(j): 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%e A359049   term:       10 4 0 1 1 0 0 0 0 0  3  1  0  0  0
%e A359049 Notice that overlapping integers are counted so 110 is one 11, one 10 (or 111 would be two 11's).
%Y A359049 Cf. A046043, A138480.
%K A359049 nonn,base
%O A359049 1,1
%A A359049 _Marc Morgenegg_, Dec 14 2022
%E A359049 a(17)-a(20) from _Michael S. Branicky_, Dec 14 2022