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%I #10 Dec 06 2019 21:45:26
%S 100,1000,101,103,104,135,171,128,119,120,109,121,256,147,239,163,304,
%T 370,340,450,240,200,150,250,600,160,130,700,170,131,812,380,168,693,
%U 379,300,110,102,106,151,167,107,108,140,111,105,112,114,115,117,118,113,126,129,123,124,125,137,122,149
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shares at least three digits with a(k). Lexicographically first sequence of positive integers without duplicate terms having this property.
%H Jean-Marc Falcoz, <a href="/A326638/b326638.txt">Table of n, a(n) for n = 1..10001</a>
%e Here are the first terms of the sequence:
%e 100,1000,101,103,104,135,171,128,119,120,...
%e and here are the cumulative sums:
%e 100,1100,1201,1304,1408,1543,1714,1842,1961,2081,...
%e If we align a(n) and its cumulative sum, we see that at least three digits are shared:
%e 100,1000, 101, 103, 104 ,135, 171, 128, 119, 120,...
%e 100,1100,1201,1304,1408,1543,1714,1842,1961,2081,...
%Y Cf. A309151 (where no digit is shared by the cumulative sum), A316914 (where one digit is shared instead of three, by the cumulative sum), A316915 (two digits shared), A326639 (four digits shared), A326640 (five digits shared).
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 15 2019