A380434 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the initial digit of n divides a(n) or the initial digit of a(n) divides n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 33, 36, 31, 39, 42, 32, 45, 48, 34, 40, 44, 35, 52, 41, 37, 56, 60, 38, 64, 50, 55, 43, 65, 61, 51, 46, 70, 75, 80, 47, 54, 66, 71, 49, 53, 62, 72

Offset: 1

Author

Rémy Sigrist, Jan 24 2025

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the positive integers.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..12000
• Rémy Sigrist, Scatterplot of the first 120000 terms
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000030, A375758.

Programs

PARI

\\ See Links section.

Python

from itertools import count, islice
def agen(): # generator of terms
    aset, m = set(), 1
    for n in count(1):
        n1 = int(str(n)[0])
        an = next(k for k in count(m) if k not in aset and (k%n1 == 0 or n%int(str(k)[0]) == 0))
        yield an
        aset.add(an)
        while m in aset: m += 1
print(list(islice(agen(), 67))) # Michael S. Branicky, Jan 27 2025