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A084383 a(0)=0; for n>0, a(n) = smallest number that is not a concatenation of any number of distinct earlier terms in increasing order.

%I A084383 #11 Aug 27 2025 09:44:44
%S A084383 0,1,2,3,4,5,6,7,8,9,10,11,20,21,22,30,31,32,33,40,41,42,43,44,50,51,
%T A084383 52,53,54,55,60,61,62,63,64,65,66,70,71,72,73,74,75,76,77,80,81,82,83,
%U A084383 84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,112,113,114,115,116,117,118,119,200,201,202
%N A084383 a(0)=0; for n>0, a(n) = smallest number that is not a concatenation of any number of distinct earlier terms in increasing order.
%C A084383 After 11 we can see 1,2 -> 12, 1,3 -> 13, etc., but not 20.
%H A084383 Michael S. Branicky, <a href="/A084383/b084383.txt">Table of n, a(n) for n = 0..10000</a>
%o A084383 (Python)
%o A084383 from itertools import islice
%o A084383 def incats(s, L):
%o A084383     if s == "": return True
%o A084383     return any(s.startswith(w) and incats(s[len(w):], L[i+1:]) for i, w in enumerate(L))
%o A084383 def agen(): # generator of terms
%o A084383     L, an, s = ["0"], 1, "1"
%o A084383     yield from [0]
%o A084383     while True:
%o A084383         yield an
%o A084383         L.append(s)
%o A084383         while incats((s:=str(an)), L):
%o A084383             an += 1
%o A084383 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Feb 01 2024
%Y A084383 Hannah Rollman's numbers: A048991, A048992.
%K A084383 nonn,base,changed
%O A084383 0,3
%A A084383 _Amarnath Murthy_, May 29 2003
%E A084383 More terms from _Patrick De Geest_, Jun 03 2003