A278437 The cumulative sum of the first successive a(n) digits is always even.

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

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

Jean-Marc 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 Jean-Marc Falcoz, Nov 22 2016

Status

approved