A362623 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the initial digit "d" of a(n) divides a(n+d).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 30, 32, 23, 27, 36, 34, 25, 33, 42, 29, 39, 38, 40, 45, 48, 31, 44, 52, 60, 35, 56, 37, 75, 41, 54, 50, 43, 64, 46, 70, 80, 47, 68, 66, 49, 72, 63, 51, 96, 78, 53, 55, 210

Offset: 1

Author

Eric Angelini, Apr 28 2023

Keywords

• base
• nonn
• look

Comments

The sequence is a permutation of the natural numbers.

Examples

			The initial digit of a(1) = 1 is 1 and 1 divides a(2) = 2;
The initial digit of a(2) = 2 is 2 and 2 divides a(4) = 4;
The initial digit of a(3) = 3 is 3 and 3 divides a(6) = 6; etc.
		

Links

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

Crossrefs

Cf. A308539.

Programs

Python

from itertools import count
from math import lcm
a = list(range(10))
while len(a) <= 100: a.append(next(k*m for k in count() if k*(m:=lcm(*[d for i in range(len(a)-9,len(a)) if (d:= int(str(a[i])[0]))+i == len(a)])) not in a))
print(a[1:]) # Dominic McCarty, Mar 12 2025

Formula

n <= a(n) < 2520*n. - Charles R Greathouse IV, Mar 13 2025

Conjecture: For n > 68, a(n) < 3*n. - Charles R Greathouse IV, Mar 13 2025

Extensions

a(54)-a(68) corrected by Dominic McCarty, Mar 12 2025