This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383217 #8 Apr 19 2025 18:07:27 %S A383217 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, %T A383217 28,29,30,32,33,34,35,36,37,40,41,44,45,46,48,49,53,54,55,56,57,59,61, %U A383217 63,64,65,66,67,68,69,70,71,76,79,80,84,85,87,90,91,97,98 %N A383217 Lexicographically earliest strictly increasing sequence such that no term is a substring of the product of all previous terms. %H A383217 Dominic McCarty, <a href="/A383217/b383217.txt">Table of n, a(n) for n = 1..10000</a> %e A383217 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. %o A383217 (Python) %o A383217 from itertools import count %o A383217 from math import prod %o A383217 a = [1] %o A383217 while len(a) < 40: a.append(next(k for k in count(a[-1]+1) if str(k) not in str(prod(a)))) %o A383217 print(a) %Y A383217 Cf. A383218 (product of first n terms), A033180. %K A383217 nonn,base %O A383217 1,2 %A A383217 _Dominic McCarty_, Apr 19 2025