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%I #8 Feb 23 2018 22:16:20
%S 3,10,17,1,2,4,6,20,30,37,5,8,40,47,7,16,48,9,11,12,13,14,15,18,38,22,
%T 50,27,23,60,19,21,70,80,28,32,67,33,68,42,57,43,58,52,24,25,26,29,36,
%U 90,100,110,107,53,49,31,69,41,59,51,54,46,34,35,39,44,78,117,63,45,55,120,87,56,61
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 3.
%C The sequence starts with a(1) = 3 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="/A300017/b300017.txt">Table of n, a(n) for n = 1..10001</a>
%e 3 shows a digit 3, of course (k = 1)
%e 3 + 10 = 13 and 13 shows at least a digit 3 (k = 2)
%e 3 + 10 + 17 = 30 and 30 shows at least a digit 3 (k = 3)
%e 3 + 10 + 17 + 1 = 31 and 31 shows at least a digit 3 (k = 4)
%e 3 + 10 + 17 + 1 + 2 = 33 and 33 shows at least a digit 3 (k = 5)
%e 3 + 10 + 17 + 1 + 2 + 4 = 37 and 37 shows at least a digit 3 (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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