A278376 The cumulative sum of the first successive a(n) digits is always odd.

1, 2, 4, 6, 3, 7, 8, 20, 9, 11, 13, 15, 17, 21, 22, 23, 27, 26, 28, 29, 30, 31, 33, 34, 36, 38, 41, 42, 46, 47, 48, 49, 50, 51, 56, 59, 61, 62, 64, 65, 72, 75, 77, 79, 83, 82, 84, 85, 86, 87, 92, 95, 97, 99, 101, 102, 104, 105, 106, 110, 111, 113, 114, 115, 117, 118, 120, 122, 124, 126, 127, 129, 131, 133, 135

Offset

1,2

Comments

The sequence starts with a(1) = 1 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, after 2000 terms, the sequence is strictly increasing except on four occasions: ..., 6, 3, ... / ..., 20, 9, ... / ..., 27, 26, ... / ..., 83, 82, ...

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..2019

Example

a(1) = 1 and the cumulative sum of the 1st digit is indeed odd (1 = 1);
a(2) = 2 and the cumulative sum of the first 2 digits is odd, too (1+2 = 3);
a(3) cannot be 3 as the cumul. sum of the first 3 digits would be even (1+2+3 = 6);
a(3) = 4 works: the cumul. sum of the first 4 digits is odd (1+2+4+6 = 13);
a(4) cannot be 3 o 5 as those cumul. sums would be even (1+2+4+3 = 10) and (1+2+4+5 = 12);
a(4) = 6 works: the cumul. sum of the first 6 digits is odd (1+2+4+6+3+7 = 23);
a(5) = 3  as the cumul. sum of the first 3 digits is now odd (1+2+4 = 7);
...
a(8) = 20 and the cumul. sum of the first 20 digits is odd (1+2+4+6+3+7+8+2+0+9+1+1+1+3+1+5+1+7+2+1 = 65);
a(9) = 9 and the cumul. sum of the first 9 digits is odd (1+2+4+6+3+7+8+2+0 = 33);
etc.

Crossrefs

Cf. A278437 (the "twin" sequence where "odd" is replaced by "even" in the definition).

Sequence in context: A327724 A117532 A287662 * A358209 A057336 A340646

Adjacent sequences: A278373 A278374 A278375 * A278377 A278378 A278379

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Nov 22 2016

Status

approved