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A300062
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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.
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3
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1, 11, 18, 19, 26, 31, 41, 42, 50, 71, 101, 201, 301, 401, 501, 601, 701, 801, 901, 1001, 1101, 1201, 1301, 1401, 1426, 1476, 1501, 1601, 1701, 1771, 1831, 1901, 2001, 2101, 2201, 2301, 2401, 2501, 2601, 2701, 2801, 2901, 3001, 3101, 3201, 3301, 3324, 3378, 3401
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OFFSET
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1,2
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COMMENTS
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1 contains 1 as a substring.
1 + 11 = 12 contains 2 as a substring and 11 is the least number > 1 that does that.
1 + 11 + 18 = 30 contains 3 as a substring and 18 is the least number > 11 that does that.
1 + 11 + 18 + 19 = 49 contains 4 as a substring and 19 is the least number > 18 that does that.
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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(Python)
for i in range(2, 10001):
j, si = j + 1, str(i)
while si not in str(s+j):
j += 1
s += j
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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