A382445 Lexicographically least increasing sequence of distinct positive integers such that for any n > 1, a(n) does not divide the concatenation of the earlier terms.

1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset

1,2

Comments

In the first 10,000 terms, there are only 6 instances in which a(n+1) is more than 1 greater than a(n). - Harvey P. Dale, Oct 18 2025

Links

Table of n, a(n) for n=1..67.

Rémy Sigrist, PARI program

Example

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

Mathematica

nxt[{c_, a_}]:=Module[{k=a+1}, While[Mod[c, k]==0, k++]; {c*10^IntegerLength[k]+k, k}]; NestList[nxt, {1, 1}, 70][[;; , 2]] (* Harvey P. Dale, Oct 18 2025 *)

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    an = t = 1
    while True:
        yield an
        an = next(k for k in count(an+1) if t%k != 0)
        t = t*10**len(str(an)) + an
print(list(islice(agen(), 54))) # Michael S. Branicky, Mar 26 2025
(PARI) \\ See Links section.

Crossrefs

Cf. A007978, A096098, A382441.

Sequence in context: A120678 A078384 A057544 * A039239 A039182 A039135

Adjacent sequences: A382442 A382443 A382444 * A382446 A382447 A382448

Keyword

nonn,base

Author

Rémy Sigrist, Mar 25 2025

Status

approved