A334929 Positive integers k such that there exists a positive integer m consisting of k identical digits and such that m is a multiple of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 18, 21, 22, 24, 27, 36, 42, 44, 45, 54, 63, 66, 72, 78, 81, 84, 88, 108, 111, 126, 132, 135, 156, 162, 168, 189, 198, 205, 216, 222, 234, 242, 243, 252, 264, 294, 312, 324, 333, 342, 378, 396, 404, 405, 444, 462, 465, 468, 484, 486

Offset

1,2

Comments

For k=3^t, t>=1 you can always find numbers m.

Links

Table of n, a(n) for n=1..61.

Example

12 is a term since 444444444444 = 12*37037037037.

Mathematica

ok[n_] := AnyTrue[(10^n - 1)/9 Range@9, Mod[#, n] == 0 &]; Select[ Range[486], ok] (* Giovanni Resta, May 24 2020 *)

Prog

(Python)
t = "1"
list = [1]
for i in range(1, 1000):
    t = "1" + t
    m = int(t)
    weiter = 0
    for k in range(1, 10):
        if k * m % (i + 1) == 0:
            weiter = 1
    if weiter == 1:
        list.append(i + 1)
print(list)

Crossrefs

Cf. A014950.

Sequence in context: A107743 A116066 A261874 * A008816 A002271 A048381

Adjacent sequences: A334926 A334927 A334928 * A334930 A334931 A334932

Keyword

nonn,base

Author

Reiner Moewald, May 16 2020

Status

approved