A326110 Lexicographically earliest sequence of distinct terms such that a(n) is divisible by four and only four digits of a(n+1).

1, 1111, 10111, 11011, 1117, 11101, 11110, 1112, 1114, 1121, 11112, 1113, 1131, 1133, 11113, 11114, 1122, 1116, 1119, 1311, 1313, 11115, 1115, 1151, 11116, 1124, 1141, 1171, 11117, 11118, 1123, 11119, 11121, 1331, 11131, 11141, 11151, 1137, 1333, 11161, 11171, 11181, 3111

Offset

1,2

Links

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

Example

The sequence starts with 1, 1111, 10111, 11011, 1117,... and we see indeed that a(2) = 1111 is the smallest available integer showing four digits that divide a(1) = 1; in the same manner we have a(3) = 10111 [the four 1s divide a(2) = 1111], a(4) = 11011 [the four 1s divide a(3) = 10111], a(5) = 1117 [all four digits divide 11011], etc.

Prog

(Python)
from itertools import count, islice
def cond(an, k):
    return 4 == 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(), 43))) # 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 A326109 [a(n) is divisible by three and only three digits of a(n+1)].

Sequence in context: A346000 A074843 A175464 * A043496 A038446 A115781

Adjacent sequences: A326107 A326108 A326109 * A326111 A326112 A326113

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jun 06 2019

Status

approved