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%I #9 Feb 23 2018 22:16:44
%S 4,10,20,6,1,2,3,8,30,40,16,5,9,50,36,7,17,60,18,12,46,11,13,14,15,19,
%T 21,31,22,28,66,24,70,80,26,34,67,23,76,44,56,54,47,33,68,32,27,25,29,
%U 35,51,43,57,53,48,42,58,52,49,41,59,61,37,63,38,62,39,64,45,72,90,100,110,116,74
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 4.
%C The sequence starts with a(1) = 4 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="/A300018/b300018.txt">Table of n, a(n) for n = 1..10001</a>
%e 4 shows a digit 4, of course (k = 1)
%e 4 + 10 = 14 and 14 shows at least a digit 4 (k = 2)
%e 4 + 10 + 20 = 34 and 34 shows at least a digit 4 (k = 3)
%e 4 + 10 + 20 + 6 = 40 and 40 shows at least a digit 4 (k = 4)
%e 4 + 10 + 20 + 6 + 1 = 41 and 41 shows at least a digit 4 (k = 5)
%e 4 + 10 + 20 + 6 + 1 + 2 = 43 and 43 shows at least a digit 4 (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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