A342077 Prime digits only come in successive pairs (separated or not by a comma).

1, 2, 20, 3, 30, 4, 5, 50, 6, 7, 70, 8, 9, 10, 11, 12, 21, 13, 31, 14, 15, 51, 16, 17, 71, 18, 19, 22, 33, 40, 41, 42, 23, 32, 24, 43, 34, 44, 45, 52, 25, 53, 35, 54, 46, 47, 72, 26, 48, 49, 55, 60, 61, 62, 27, 73, 36, 63, 37, 74, 64, 65, 56, 66, 67, 75, 57, 76, 68, 69, 77, 80, 81, 82, 28, 83, 38

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(2) = 2 forces the next digit to be a 2 (as prime digits must come in pairs); the smallest positive integer not yet present that starts with a 2 is 20. Thus, a(3) = 20;
a(4) = 3 as 3 is the smallest positive integer not yet present that does not lead to a contradiction;
a(5) = 30 as 30 is the smallest positive integer not yet present that does not lead to a contradiction and starts with a 3; etc.
		

Crossrefs

Cf. A342076, A342078 and A342079 (variations on the same idea)

Programs

Python

# see A342076 for aupton, pairsup
mustpair = {2, 3, 5, 7}
print(aupton(67)) # Michael S. Branicky, Feb 28 2021