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%I #15 Nov 22 2016 21:43:47
%S 2,4,1,5,6,8,9,10,20,11,13,15,17,22,21,19,24,29,31,33,35,37,39,40,41,
%T 42,47,48,49,50,52,53,56,58,59,62,67,68,69,70,72,73,76,78,79,82,87,88,
%U 89,90,92,93,96,98,99,102,104,105,106,110,111,113,114,115,117,118,120,122,124,126,127,129,131,133
%N The cumulative sum of the first successive a(n) digits is always even.
%C The sequence starts with a(1) = 2 and is always extended with the smallest positive integer not yet present that does not lead to a contradiction.
%C This is the lexicographically first sequence with this property.
%C Amazingly, for the first 1500 terms, the sequence is strictly increasing except on four occasions: ..., 4, 1, ... / ..., 20, 11, ... / ..., 22, 21, ... / ..., 21, 19, ...
%H Jean-Marc Falcoz, <a href="/A278437/b278437.txt">Table of n, a(n) for n = 1..1514</a>
%e a(1) = 2 and the cumulative sum of the first 2 digits is indeed even (2+4 = 6).
%e a(2) = 4 and the cumulative sum of the first 4 digits is even (2+4+1+5).
%e a(3) = 1 and the cumulative sum of the 1st digit is of course even (2=2).
%e a(4) cannot be 3 as the cumul. sum of the first 3 digits would be odd (2+4+3 = 9).
%e a(4) = 5 works and the cumul. sum of the first 5 digits is indeed even (2+4+1+5+6 = 18).
%e a(5) = 6 works and the cumul. sum of the first 6 digits is indeed even (2+4+1+5+6+8= 26).
%e ...
%e a(8) = 10 and the cumul. sum of the first 10 digits is even (2+4+1+5+6+8+9+1+0+2 = 38).
%Y Cf. A278376 (the "twin" sequence where "even" is replaced by "odd" in the definition).
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Nov 22 2016
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