A263314 Numbers m whose decimal representation includes at least one digit that divides every digit of m.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 30, 31, 33, 36, 39, 40, 41, 42, 44, 48, 50, 51, 55, 60, 61, 62, 63, 66, 70, 71, 77, 80, 81, 82, 84, 88, 90, 91, 93, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112

Offset: 1

Author

Giovanni Teofilatto, Oct 14 2015

Keywords

• nonn
• base

Comments

Every number that has a digit '1' (cf. A011531) is in this sequence. Sequence A034838 (every digit divides n) is not a subsequence (e.g., 324 is not in the present sequence). - M. F. Hasler, Jan 10 2016

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Programs

PARI

is(n)={n && (n=select(t->t,Set(digits(n))))%n[1]==0} \\ The divisor is necessarily the smallest nonzero digit. A vector having no nonzero component is considered equal to 0. - M. F. Hasler, Jan 10 2016

Python

A263314_list = []
for i in range(10**4):
    s = str(i)
    for d in s:
        j = int(d)
        if j :
            for e in s:
                if int(e) % j:
                    break
            else:
                A263314_list.append(i)
                break
# Chai Wah Wu, Oct 21 2015