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A260351 In base n, a(n) is the largest (decimal equivalent) number reached when one sequentially adds to a sum, starting with zero, the largest digit not in that sum.

%I A260351 #29 May 22 2025 10:21:43
%S A260351 1,5,30,214,1865,22881,342447,6053444,123456798,2853116815,
%T A260351 73686782411,2103299351346,65751519678065,2234152501943369,
%U A260351 81985529216487165,3231407272993503256,136146740744970718253,6106233505124424781971,290464265927977839351196
%N A260351 In base n, a(n) is the largest (decimal equivalent) number reached when one sequentially adds to a sum, starting with zero, the largest digit not in that sum.
%H A260351 Hiroaki Yamanouchi, <a href="/A260351/b260351.txt">Table of n, a(n) for n = 2..22</a>
%H A260351 Frank Adams-Watters, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-July/015118.html">Add the biggest absent digit</a>, SeqFan list, July 21, 2015
%e A260351 In base 4:
%e A260351 0 + 3 = 3 (= 3)
%e A260351 3 + 2 = 5 (= 11)
%e A260351 5 + 3 = 8 (= 20)
%e A260351 8 + 3 = 11 (= 23)
%e A260351 11 + 1 = 12 (= 30)
%e A260351 12 + 2 = 14 (= 32)
%e A260351 14 + 1 = 15 (= 33)
%e A260351 15 + 2 = 17 (= 101)
%e A260351 17 + 3 = 20 (= 110)
%e A260351 20 + 3 = 23 (= 113)
%e A260351 23 + 2 = 25 (= 121)
%e A260351 25 + 3 = 28 (= 130)
%e A260351 28 + 2 = 30 (= 132)
%e A260351 30 + 0 = 30 (repeat, therefore a(4) = 30)
%t A260351 Table[r=Range[0, b-1]; s=0; t=1; While[t!=0, t=Complement[r, IntegerDigits[s, b]][[-1]]; s=s+t]; s, {b, 2, 8}]
%o A260351 (Python)
%o A260351 from gmpy2 import digits
%o A260351 def A260351(n):
%o A260351     r, c = set([digits(d,n) for d in range(n)]), 0
%o A260351     dc = set(digits(c,n))
%o A260351     while len(dc) < n-1 or '0' in dc:
%o A260351         c += max([int(d,n) for d in r - dc])
%o A260351         dc = set(digits(c,n))
%o A260351     return c # _Chai Wah Wu_, Jul 24 2015
%Y A260351 Cf. A260263, A260264.
%K A260351 nonn,base
%O A260351 2,2
%A A260351 _Hans Havermann_, Jul 23 2015
%E A260351 a(13) from _Giovanni Resta_, Jul 23 2015
%E A260351 a(14) from _Giovanni Resta_, Jul 24 2015
%E A260351 a(15)-a(20) from _Hiroaki Yamanouchi_, Aug 01 2015