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A300016 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 2. 1

%I

%S 2,10,8,1,3,4,14,20,30,28,5,7,40,29,6,9,11,12,13,15,16,19,18,22,50,31,

%T 39,58,32,60,17,23,68,42,59,21,70,80,33,27,69,41,38,24,25,26,37,90,

%U 100,110,108,52,48,62,43,47,34,35,36,44,45,46,49,51,53,54,55,56,57,61,63,64,65,66,67

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

%C The sequence starts with a(1) = 2 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="/A300016/b300016.txt">Table of n, a(n) for n = 1..10001</a>

%e 2 shows a digit 2, of course (k = 1)

%e 2 + 10 = 12 and 12 shows at least a digit 2 (k = 2)

%e 2 + 10 + 8 = 20 and 20 shows at least a digit 2 (k = 3)

%e 2 + 10 + 8 + 1 = 21 and 21 shows at least a digit 2 (k = 4)

%e 2 + 10 + 8 + 1 + 3 = 24 and 24 shows at least a digit 2 (k = 5)

%e 2 + 10 + 8 + 1 + 3 + 4 = 28 and 28 shows at least a digit 2 (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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Last modified September 22 14:32 EDT 2021. Contains 347607 sequences. (Running on oeis4.)