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%I #8 Feb 23 2018 22:17:29
%S 10,20,30,40,1,2,3,4,50,41,5,14,60,21,6,13,70,11,7,12,80,8,22,71,9,90,
%T 100,101,19,81,15,16,17,18,23,110,102,28,72,38,61,29,73,27,74,26,75,
%U 25,76,24,77,31,32,33,37,62,48,51,39,63,47,52,58,42,68,34,36,64,46,53,57,43,35,44,78
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 0.
%C The sequence starts with a(1) = 10 and is always extended with the smallest integer not yet present that does not lead to a contradiction.
%C A permutation of the natural numbers.
%H Jean-Marc Falcoz, <a href="/A300024/b300024.txt">Table of n, a(n) for n = 1..10001</a>
%e 10 shows at least a digit 0, of course (k = 1)
%e 10 + 20 = 30 and 30 shows at least a digit 0 (k = 2)
%e 10 + 20 + 30 = 60 and 60 shows at least a digit 0 (k = 3)
%e 10 + 20 + 30 + 40 = 100 and 100 shows at least a digit 0 (k = 4)
%e 10 + 20 + 30 + 40 + 1 = 101 and 101 shows at least a digit 0 (k = 5)
%e 10 + 20 + 30 + 40 + 1 + 2 = 103 and 103 shows at least a digit 0 (k = 6)
%e ...
%Y Cf. A300015 (which is the lexicographic first sequence of positive integers without duplicate terms having this property).
%K nonn,base
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 23 2018
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