A326108 Lexicographically earliest sequence of distinct terms such that a(n) is divisible by two and only two digits of a(n+1).

1, 11, 101, 110, 12, 13, 112, 14, 17, 113, 114, 16, 18, 19, 115, 15, 31, 116, 21, 33, 103, 117, 39, 118, 22, 102, 23, 119, 71, 121, 131, 141, 123, 130, 25, 51, 132, 24, 26, 120, 28, 27, 91, 77, 107, 151, 161, 127, 171, 93, 134, 124, 41, 181, 191, 211, 311, 411, 135, 35, 55, 105, 37, 511, 137, 611, 711, 99

Offset

1,2

Comments

The first term that does not show any digit 1 is a(20) = 33.

Links

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

Example

The sequence starts with 1, 11, 101, 110, 12, 13, 112, 14,... and we see indeed that a(2) = 11 is the smallest available integer showing two digits that divide a(1) = 1; in the same manner we have a(3) = 101 and a(4) = 110; a(5) = 12 because 12 is the smallest available integer that has two digits dividing a(4); etc.

Prog

(PARI) s=0; v=1; for (n=1, 68, print1 (v", "); s+=2^v; for (w=1, oo, if (!bittest(s, w) && #select(d -> d && v%d==0, digits(w))==2, v=w; break))) \\ Rémy Sigrist, Jul 11 2019
(Python)
from itertools import count, islice
def cond(an, k):
    return 2 == 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(), 68))) # 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)], A326109 [a(n) is divisible by three and only three digits of a(n+1)] and A326110 [a(n) is divisible by four and only four digits of a(n+1)].

Sequence in context: A391444 A377370 A133835 * A292451 A292731 A225534

Adjacent sequences: A326105 A326106 A326107 * A326109 A326110 A326111

Keyword

base,nonn,look

Author

Eric Angelini and Carole Dubois, Jun 06 2019

Status

approved