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A300062 a(1) = 1, a(n) = the smallest integer > a(n-1) such that Sum_{k=1..n} a(k) written in decimal contains decimal n as a substring.

%I A300062 #13 Jan 01 2020 22:05:41
%S A300062 1,11,18,19,26,31,41,42,50,71,101,201,301,401,501,601,701,801,901,
%T A300062 1001,1101,1201,1301,1401,1426,1476,1501,1601,1701,1771,1831,1901,
%U A300062 2001,2101,2201,2301,2401,2501,2601,2701,2801,2901,3001,3101,3201,3301,3324,3378,3401
%N A300062 a(1) = 1, a(n) = the smallest integer > a(n-1) such that Sum_{k=1..n} a(k) written in decimal contains decimal n as a substring.
%C A300062 1 contains 1 as a substring.
%C A300062 1 + 11 = 12 contains 2 as a substring and 11 is the least number > 1 that does that.
%C A300062 1 + 11 + 18 = 30 contains 3 as a substring and 18 is the least number > 11 that does that.
%C A300062 1 + 11 + 18 + 19 = 49 contains 4 as a substring and 19 is the least number > 18 that does that.
%C A300062 In the first 10000 terms the distribution of the least significant digit {0-9} is {201, 8339, 189, 185, 184, 174, 183, 176, 179, 190}. - _Robert G. Wilson v_, Feb 24 2018
%H A300062 Chai Wah Wu, <a href="/A300062/b300062.txt">Table of n, a(n) for n = 1..10000</a>
%t A300062 f[lst_List] := Block[{k = 1 + lst[[-1]], n = ToString[1 + Length@lst], s = Plus @@ lst}, While[StringPosition[ToString[s + k], n] == {}, k++]; Append[lst, k]]; Nest[f, {1}, 50] (* _Robert G. Wilson v_, Feb 24 2018 *)
%o A300062 (Python)
%o A300062 A300062_list, s, j = [1], 1, 1
%o A300062 for i in range(2,10001):
%o A300062     j, si = j + 1, str(i)
%o A300062     while si not in str(s+j):
%o A300062         j += 1
%o A300062     A300062_list.append(j)
%o A300062     s += j
%Y A300062 Cf. A162555.
%K A300062 nonn,base
%O A300062 1,2
%A A300062 _Chai Wah Wu_, Feb 23 2018