A342078 Odd digits only come in successive pairs (separated or not by a comma).

1, 10, 2, 3, 30, 4, 5, 50, 6, 7, 70, 8, 9, 90, 11, 20, 21, 12, 22, 23, 31, 13, 32, 24, 25, 51, 14, 26, 27, 71, 15, 52, 28, 29, 91, 16, 33, 40, 41, 17, 72, 42, 43, 34, 44, 45, 53, 35, 54, 46, 47, 73, 36, 48, 49, 92, 55, 60, 61, 18, 62, 63, 37, 74, 64, 65, 56, 66, 67, 75, 57, 76, 68

Offset: 1

Author

Eric Angelini, Feb 28 2021

Keywords

• base
• nonn

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.

Examples

			a(1) = 1 forces the next digit to be a 1 (as odd digits must come in pairs); the smallest positive integer not yet present that starts with a 1 and does not lead to a contradiction is 10. Thus, a(2) = 10;
a(3) = 2 as the smallest positive integer not yet present that does not lead to a contradiction is 2;
a(4) = 3 as the smallest positive integer not yet present that does not lead to a contradiction is 3;
a(5) = 30 as a(5) must start with a 3 (the odd digits must come in pairs) and 30 is the smallest positive integer not yet present that does not lead to a contradiction; etc.
		

Crossrefs

Cf. A342076, A342077 and A342079 (variations on the same idea).

Programs

Python

# see A342076 for aupton, pairsup
mustpair = {1, 3, 5, 7, 9}
print(aupton(67)) # Michael S. Branicky, Feb 28 2021