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%I #12 Feb 24 2018 11:56:56
%S 8,10,20,30,12,1,2,3,22,40,32,4,5,9,50,33,6,11,60,23,7,70,24,16,80,90,
%T 13,17,82,18,14,15,19,21,25,26,62,28,72,38,63,27,73,37,64,36,65,35,66,
%U 34,67,43,52,29,31,39,49,53,47,54,46,55,45,56,44,57,83,100,110,102,41,42,75,48,92
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 8.
%C The sequence starts with a(1) = 8 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="/A300022/b300022.txt">Table of n, a(n) for n = 1..10001</a>
%e 8 shows a digit 8, of course (k = 1)
%e 8 + 10 = 18 and 18 shows at least a digit 8 (k = 2)
%e 8 + 10 + 20 = 38 and 38 shows at least a digit 8 (k = 3)
%e 8 + 10 + 20 + 30 = 68 and 68 shows at least a digit 8 (k = 4)
%e 8 + 10 + 20 + 30 + 12 = 80 and 80 shows at least a digit 8 (k = 5)
%e 8 + 10 + 20 + 30 + 12 + 1 = 81 and 81 shows at least a digit 8 (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