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

Author

Rémy Sigrist, Mar 25 2025

Keywords

• nonn
• base

Examples

			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.
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A007978, A096098, A382441.

Programs

PARI

\\ See Links section.

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