A326109 Lexicographically earliest sequence of distinct terms such that a(n) is divisible by three and only three digits of a(n+1).

1, 111, 113, 1011, 131, 1101, 133, 117, 119, 171, 139, 1110, 112, 114, 116, 121, 1112, 118, 122, 211, 1113, 137, 1114, 212, 124, 141, 311, 1115, 115, 151, 1116, 123, 313, 1117, 1118, 221, 1119, 331, 1121, 1131, 333, 191, 1141, 177, 1013, 1151, 1161, 193, 1171, 1181, 1191, 1031, 1211, 711, 199, 1311

Offset

1,2

Links

Carole Dubois, Table of n, a(n) for n = 1..5000

Example

The sequence starts with 1, 111, 113, 1011, 131, 1101, 133, ... and we see indeed that a(2) = 111 is the smallest available integer showing three digits that divide a(1) = 1; in the same manner we have a(3) = 113 [all three digits divide 111], a(4) = 1011 [the three 1s of 1011 divide 113], a(5) = 131 [all three digits divide 1011], etc.

Prog

(Python)
from itertools import count, islice
def cond(an, k):
    return 3 == sum(1 for d in map(int, str(k)) if d and an%d == 0)
def agen(): # generator of terms
    an, m, aset = 1, 2, set()
    while True:
        yield an
        aset.add(an)
        an = next(k for k in count(m) if k not in aset and cond(an, k))
        while m in aset: m += 1
print(list(islice(agen(), 56))) # Michael S. Branicky, May 04 2026

Crossrefs

Cf. A326106 [a(n) is not divisible by any digit of a(n+1)], A326107 [a(n) is divisible by one and only one digit of a(n+1)], A326108 [a(n) is divisible by two and only two digits of a(n+1)] and A326110 [a(n) is divisible by four and only four digits of a(n+1)].

Sequence in context: A395128 A133786 A211683 * A338111 A351060 A208260

Adjacent sequences: A326106 A326107 A326108 * A326110 A326111 A326112

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jun 06 2019

Status

approved