A383217 Lexicographically earliest strictly increasing sequence such that no term is a substring of the product of all previous terms.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 40, 41, 44, 45, 46, 48, 49, 53, 54, 55, 56, 57, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 76, 79, 80, 84, 85, 87, 90, 91, 97, 98

Offset: 1

Author

Dominic McCarty, Apr 19 2025

Keywords

• nonn
• base

Examples

			The product of the first 6 terms is 720. "7" is a substring of "720", so a(7) cannot be 7. So, a(7) is the next available value, 8.
		

Links

• Dominic McCarty, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A383218 (product of first n terms), A033180.

Programs

Python

from itertools import count
from math import prod
a = [1]
while len(a) < 40: a.append(next(k for k in count(a[-1]+1) if str(k) not in str(prod(a))))
print(a)