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A368181 a(1) = 1; for n > 1, a(n) is the smallest positive integer that has not yet appeared which shares no digit with the sum of all previous terms a(1)..a(n-1).

%I A368181 #34 Dec 22 2023 08:35:30
%S A368181 1,2,4,3,5,6,7,9,8,10,11,12,13,20,22,24,23,25,14,30,15,17,33,26,16,18,
%T A368181 19,21,27,28,31,29,34,40,41,32,35,36,38,39,37,42,44,50,43,52,45,46,47,
%U A368181 48,49,54,55,57,56,60,53,58,59,62,63,65,70,51,61,64,66,67,69,68,71,73,74,81,90,91,77
%N A368181 a(1) = 1; for n > 1, a(n) is the smallest positive integer that has not yet appeared which shares no digit with the sum of all previous terms a(1)..a(n-1).
%C A368181 The sequence is finite; after 14594 terms, where a(14594) = 20858, the sum of all terms is 173658294 which contains the digits 1..9, so the next term does not exist.
%C A368181 The largest term is a(12742) = 888888.
%H A368181 Scott R. Shannon, <a href="/A368181/b368181.txt">Table of n, a(n) for n = 1..14594</a>
%e A368181 a(14) = 20 as the sum of all terms a(1)..a(13) = 91, and 20 is the smallest unused number that does not contain the digits 1 or 9.
%o A368181 (Python)
%o A368181 from itertools import islice
%o A368181 def agen():
%o A368181   s, aset, mink = 0, {0}, 1
%o A368181   while True:
%o A368181       k, dset = mink, set(str(s))
%o A368181       if dset >= set("123456789"): break
%o A368181       while k in aset or set(str(k)) & dset: k += 1
%o A368181       an = k; aset.add(an); s += an; yield an
%o A368181       while mink in aset: mink += 1
%o A368181 print(list(islice(agen(), 80))) # _Michael S. Branicky_, Dec 21 2023
%Y A368181 Cf. A362093, A362075, A342383, A342382.
%K A368181 nonn,base,fini,full
%O A368181 1,2
%A A368181 _Scott R. Shannon_, Dec 21 2023