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For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 6.
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%I #8 Feb 23 2018 22:16:59

%S 6,10,20,24,1,2,3,30,40,25,4,11,50,34,5,21,60,14,7,9,70,15,8,17,74,16,

%T 26,12,13,18,19,22,75,35,64,36,65,45,54,46,55,85,23,27,66,44,56,84,57,

%U 28,29,31,69,76,32,38,58,42,59,41,61,39,62,48,47,33,67,43,63,37,49,51,80,77,53,52

%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 6.

%C The sequence starts with a(1) = 6 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="/A300020/b300020.txt">Table of n, a(n) for n = 1..10001</a>

%e 6 shows a digit 6, of course (k = 1)

%e 6 + 10 = 16 and 16 shows at least a digit 6 (k = 2)

%e 6 + 10 + 20 = 36 and 36 shows at least a digit 6 (k = 3)

%e 6 + 10 + 20 + 24 = 60 and 60 shows at least a digit 6 (k = 4)

%e 6 + 10 + 20 + 24 + 1 = 61 and 61 shows at least a digit 6 (k = 5)

%e 6 + 10 + 20 + 24 + 1 + 2 = 63 and 63 shows at least a digit 6 (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