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

1,2

Links

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

Example

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.

Prog

(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)

Crossrefs

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

Sequence in context: A004726 A298747 A327105 * A356451 A129618 A349536

Adjacent sequences: A383214 A383215 A383216 * A383218 A383219 A383220

Keyword

nonn,base

Author

Dominic McCarty, Apr 19 2025

Status

approved