A383322 Lexicographically earliest sequence of distinct terms such that replacing each term k with k! does not change the succession of digits.

1, 2, 198, 15, 5, 24, 3, 0, 56, 4, 800, 260, 18, 181, 7, 120, 43, 26, 25, 78, 46, 6, 11, 45, 67, 2580, 8, 37, 34, 49, 61, 66, 465, 63, 9, 28, 62, 93, 960, 65, 410, 626, 13, 82, 98, 59, 32, 659, 453, 242, 255, 580, 939, 42, 70, 44, 932, 22, 55, 38, 389, 50

Offset: 1

Author

Dominic McCarty, Apr 23 2025

Keywords

• nonn
• base

Comments

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.

Examples

			Let b(n) = a(n)!
(a(n)): 1, 2, 198, 15, 5, 24, 3, 0, 56, 4, 800, 260, 18, ...
(b(n)): 1, 2, 198155243056480026018[...] (350 digits omitted), ...
		

Links

• Dominic McCarty, Table of n, a(n) for n = 1..10000
• Dominic McCarty, Table of n, a(n)! for n = 1..100

Crossrefs

Cf. A033147, A383318, A383320, A302656.

Programs

Python

from sympy import factorial
from itertools import count
a, sa, sb = [1, 2, 198], "12198", "12"+str(factorial(198))
for _ in range(20):
    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"))))
    sa += str(a[-1]); sb += str(factorial(a[-1]))
print(a)