This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375969 #16 Sep 08 2024 21:41:10
%S A375969 0,1,2,3,4,5,6,7,8,9,10,12,14,16,18,29,49,69,89,100,101,103,104,106,
%T A375969 107,109,119,139,149,169,179,199,299,499,599,799,899,1000,1002,1004,
%U A375969 1006,1008,1019,1039,1059,1079,1099,1299,1499,1699,1899,2999,4999,6999
%N A375969 Lexicographically earliest sequence of nonnegative integers with distinct digit averages.
%C A375969 Equivalently, fixed points of A375968.
%C A375969 The sequence {A007953(a(n)) / A055642(a(n)), n > 0} runs uniquely through every rational number between 0 and 9.
%H A375969 Rémy Sigrist, <a href="/A375969/b375969.txt">Table of n, a(n) for n = 1..10459</a>
%H A375969 Rémy Sigrist, <a href="/A375969/a375969.gp.txt">PARI program</a>
%e A375969 The first terms, alongside the corresponding digit average, are:
%e A375969 n a(n) Digit average
%e A375969 -- ---- -------------
%e A375969 1 0 0
%e A375969 2 1 1
%e A375969 3 2 2
%e A375969 4 3 3
%e A375969 5 4 4
%e A375969 6 5 5
%e A375969 7 6 6
%e A375969 8 7 7
%e A375969 9 8 8
%e A375969 10 9 9
%e A375969 11 10 1/2
%e A375969 12 12 3/2
%e A375969 13 14 5/2
%e A375969 14 16 7/2
%e A375969 15 18 9/2
%t A375969 kmax=7000; avg={}; list={}; For[k=0, k<=kmax, k++,mn=Mean[IntegerDigits[k]]; If[!MemberQ[avg,mn], AppendTo[avg, mn]; AppendTo[list, k]]]; list (* _Stefano Spezia_, Sep 07 2024 *)
%o A375969 (PARI) avg(n, base = 10) = { my (d = digits(n, base)); vecsum(d) / max(1, #d) }
%o A375969 { V = Map(); k = 0; for (n = 0, 6999, v = avg(n); if (!mapisdefined(V, v), mapput(V, v, n); print1 (n", "););); }
%o A375969 (PARI) \\ See Links section.
%o A375969 (Python)
%o A375969 from math import gcd
%o A375969 from itertools import count, islice
%o A375969 def agen():
%o A375969 m = 0
%o A375969 yield 0
%o A375969 for w in count(1): # w = number of digits
%o A375969 for s in range(1, 9*w+1): # s = sum of digits
%o A375969 if gcd(s, w) == 1:
%o A375969 d, r = [1] + [0 for _ in range(w-1)], s-1
%o A375969 for k in range(w-1, -1, -1):
%o A375969 d[k], r = d[k] + min(r, 9), r - min(r, 9)
%o A375969 yield int("".join(map(str, d)))
%o A375969 print(list(islice(agen(), 54)))
%o A375969 # _Michael S. Branicky_, Sep 08 2024 after _Rémy Sigrist_ PARI in link
%Y A375969 Cf. A007953, A051885, A055642, A375968.
%K A375969 nonn,base
%O A375969 1,3
%A A375969 _Rémy Sigrist_, Sep 04 2024