%I
%S 5,10,20,15,1,2,3,9,30,40,16,4,50,45,6,19,60,17,7,26,65,8,27,18,11,12,
%T 13,14,21,22,29,25,35,66,24,70,80,28,32,67,23,75,55,46,34,68,42,56,44,
%U 31,33,36,57,43,58,52,47,53,48,62,37,63,38,72,90,39,41,59,49,51,61,100,110,120,105,85,115,95,106,54,64,76,107,73,125,101,74,126,84,116,69,71,94,130
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 5.
%C The sequence starts with a(1) = 5 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 JeanMarc Falcoz, <a href="/A300019/b300019.txt">Table of n, a(n) for n = 1..10001</a>
%e 5 shows a digit 5, of course (k = 1)
%e 5 + 10 = 15 and 15 shows at least a digit 5 (k = 2)
%e 5 + 10 + 20 = 35 and 35 shows at least a digit 5 (k = 3)
%e 5 + 10 + 20 + 15 = 50 and 50 shows at least a digit 5 (k = 4)
%e 5 + 10 + 20 + 15 + 1 = 51 and 51 shows at least a digit 5 (k = 5)
%e 5 + 10 + 20 + 15 + 1 + 2 = 53 and 53 shows at least a digit 5 (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 _JeanMarc Falcoz_, Feb 23 2018
