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 A383322 #11 Apr 24 2025 15:14:55 %S A383322 1,2,198,15,5,24,3,0,56,4,800,260,18,181,7,120,43,26,25,78,46,6,11,45, %T A383322 67,2580,8,37,34,49,61,66,465,63,9,28,62,93,960,65,410,626,13,82,98, %U A383322 59,32,659,453,242,255,580,939,42,70,44,932,22,55,38,389,50 %N A383322 Lexicographically earliest sequence of distinct terms such that replacing each term k with k! does not change the succession of digits. %C A383322 Similarly to A302656, this sequence contains very large jumps. For example, a(131) = 4*10^47, a(702) = 496*10^199, a(2808) = 5712*10^643, etc. %H A383322 Dominic McCarty, <a href="/A383322/b383322.txt">Table of n, a(n) for n = 1..10000</a> %H A383322 Dominic McCarty, <a href="/A383322/a383322.txt">Table of n, a(n)! for n = 1..100</a> %e A383322 Let b(n) = a(n)! %e A383322 (a(n)): 1, 2, 198, 15, 5, 24, 3, 0, 56, 4, 800, 260, 18, ... %e A383322 (b(n)): 1, 2, 198155243056480026018[...] (350 digits omitted), ... %o A383322 (Python) %o A383322 from sympy import factorial %o A383322 from itertools import count %o A383322 a, sa, sb = [1, 2, 198], "12198", "12"+str(factorial(198)) %o A383322 for _ in range(20): %o A383322 a.append(next(n for k in count(1) if not (n := int(sb[len(sa):len(sa)+k])) in a and (0 not in a or not (len(sb) > len(sa) + k and sb[len(sa) + k] == "0")))) %o A383322 sa += str(a[-1]); sb += str(factorial(a[-1])) %o A383322 print(a) %Y A383322 Cf. A033147, A383318, A383320, A302656. %K A383322 nonn,base %O A383322 1,2 %A A383322 _Dominic McCarty_, Apr 23 2025