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A278376 The cumulative sum of the first successive a(n) digits is always odd. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A057336 A236675 A210771

Adjacent sequences:  A278373 A278374 A278375 * A278377 A278378 A278379

KEYWORD

nonn,base

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Nov 22 2016

STATUS

approved

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Last modified May 31 00:06 EDT 2020. Contains 334747 sequences. (Running on oeis4.)