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

1,2

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

Prog

(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

Crossrefs

Cf. A000030, A375758.

Sequence in context: A089867 A089870 A089869 * A358121 A335524 A338555

Adjacent sequences: A380431 A380432 A380433 * A380435 A380436 A380437

Keyword

nonn,base

Author

Rémy Sigrist, Jan 24 2025

Status

approved