

A278437


The cumulative sum of the first successive a(n) digits is always even.


2



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, 42, 47, 48, 49, 50, 52, 53, 56, 58, 59, 62, 67, 68, 69, 70, 72, 73, 76, 78, 79, 82, 87, 88, 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
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OFFSET

1,1


COMMENTS

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.
This is the lexicographically first sequence with this property.
Amazingly, for the first 1500 terms, the sequence is strictly increasing except on four occasions: ..., 4, 1, ... / ..., 20, 11, ... / ..., 22, 21, ... / ..., 21, 19, ...


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..1514


EXAMPLE

a(1) = 2 and the cumulative sum of the first 2 digits is indeed even (2+4 = 6).
a(2) = 4 and the cumulative sum of the first 4 digits is even (2+4+1+5).
a(3) = 1 and the cumulative sum of the 1st digit is of course even (2=2).
a(4) cannot be 3 as the cumul. sum of the first 3 digits would be odd (2+4+3 = 9).
a(4) = 5 works and the cumul. sum of the first 5 digits is indeed even (2+4+1+5+6 = 18).
a(5) = 6 works and the cumul. sum of the first 6 digits is indeed even (2+4+1+5+6+8= 26).
...
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).


CROSSREFS

Cf. A278376 (the "twin" sequence where "even" is replaced by "odd" in the definition).
Sequence in context: A283741 A094640 A070937 * A175036 A177985 A198512
Adjacent sequences: A278434 A278435 A278436 * A278438 A278439 A278440


KEYWORD

base,nonn


AUTHOR

Eric Angelini and JeanMarc Falcoz, Nov 22 2016


STATUS

approved



