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
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
Programs
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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)