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%I #10 Jul 26 2019 18:51:58
%S 10,100,11,13,14,16,18,20,12,23,26,29,32,35,39,24,46,51,45,40,67,74,
%T 27,19,21,90,101,30,41,106,15,61,17,31,33,37,84,50,56,62,69,47,81,91,
%U 102,60,71,92,22,28,112,34,42,25,52,117,72,82,38,95,80,103,43,73,133,36,93,53,63,70,78,83,59,49,104
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shares at least two digits with a(k). Lexicographic first sequence of positive integers without duplicate terms having this property.
%H Jean-Marc Falcoz, <a href="/A316915/b316915.txt">Table of n, a(n) for n = 1..10001</a>
%e Here are the first terms of the sequence:
%e 10,100,11,13,14,16,18,20,12,23,26,29,32,...
%e and here are the cumulative sums:
%e 10,110,121,134,148,162,180,200,212,235,261,290,322,...
%e If we align a(n) and its cumulative sum, we see that at least two digits are shared:
%e 10,100, 11, 13, 14, 16, 18, 20, 12, 23, 26, 29, 32,...
%e 10,110,121,134,148,162,180,200,212,235,261,290,322,...
%Y Cf. A316914 (where one digit is shared instead of two, by the cumulative sum).
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 16 2018
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