A382441 Lexicographically earliest sequence of positive integers such that for any n > 1, a(n) does not divide any of the positive numbers whose decimal expansion appears as a contiguous subword in the concatenation of the previous terms.

1, 2, 5, 7, 8, 9, 10, 16, 20, 32, 40, 50, 51, 53, 64, 83, 93, 100, 117, 118, 126, 160, 186, 200, 207, 224, 250, 288, 311, 320, 352, 372, 391, 400, 448, 480, 500, 625, 640, 713, 800, 960, 979, 1000, 1011, 1039, 1043, 1097, 1099, 1173, 1200, 1250, 1359, 1426

Offset

1,2

Comments

This sequence contains all powers of 10.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1000

Rémy Sigrist, C++ program

Example

a(1) = 1.
a(2) must not divide 1; we can take a(2) = 2.
a(3) must not divide 1, 2 or 12; we can take a(3) = 5.

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    an, s, d = 1, "1", [1]
    while True:
        yield an
        an = next(k for k in count(an+1) if not any(di%k == 0 for di in d))
        for di in str(an):
            s += di
            d += [si for i in range(len(s)) if (si:=int(s[i:])) > an]
        d = sorted(set(d))
print(list(islice(agen(), 54))) # Michael S. Branicky, Mar 26 2025
(C++) // See Links section.

Crossrefs

Cf. A048991, A382442 (binary variant), A382445.

Sequence in context: A186306 A047483 A339309 * A167408 A047388 A284529

Adjacent sequences: A382438 A382439 A382440 * A382442 A382443 A382444

Keyword

nonn,base

Author

Rémy Sigrist, Mar 25 2025

Status

approved