A342079 Even digits only come in successive pairs (separated or not by a comma).

1, 2, 21, 3, 4, 41, 5, 6, 61, 7, 8, 81, 9, 11, 12, 22, 23, 13, 14, 42, 24, 43, 15, 16, 62, 25, 17, 18, 82, 26, 63, 19, 31, 32, 27, 33, 34, 44, 45, 35, 36, 64, 46, 65, 37, 38, 83, 39, 51, 52, 28, 84, 47, 53, 54, 48, 85, 55, 56, 66, 67, 57, 58, 86, 68, 87, 59, 71, 72, 29, 73, 74, 49, 75, 76, 69, 77, 78, 88, 89

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.

No term can end with an odd number of successive 0.

Links

Table of n, a(n) for n=1..80.

Example

a(2) = 2 as the smallest positive integer not yet present that does not lead to a contradiction is 2;
a(3) = 21 (and not 20, as no term can end with an odd number of successive 0), because 21 is the smallest positive integer not yet present that completes a pair of identical even digits (2-2) and that does not lead to a contradiction;
a(4) = 3 as the smallest positive integer not yet present that does not lead to a contradiction is 3;
a(5) = 4 as the smallest positive integer not yet present that does not lead to a contradiction is 4;
a(6) = 41 (and not 40, as no term can end with an odd number of successive 0), because 41 is the smallest positive integer not yet present that completes a pair of identical even digits (4-4) and that does not lead to a contradiction; etc.

Prog

(Python) # see A342076 for aupton, pairsup
mustpair = {0, 2, 4, 6, 8}
print(aupton(67)) # Michael S. Branicky, Feb 28 2021

Crossrefs

Cf. A342076, A342077 and A342078 (variations on the same idea).

Sequence in context: A249646 A143247 A395172 * A303216 A331460 A303218

Adjacent sequences: A342076 A342077 A342078 * A342080 A342081 A342082

Keyword

base,nonn

Author

Eric Angelini, Feb 28 2021

Status

approved