A368955 Numbers that are the product of two repdigit numbers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 54, 55, 56, 63, 64, 66, 72, 77, 81, 88, 99, 110, 111, 121, 132, 154, 165, 176, 198, 220, 222, 231, 242, 264, 275, 297, 308, 330, 333

Offset: 1

Author

Stefano Spezia, Jan 10 2024

Keywords

• nonn
• base
• easy

Comments

A010785 and A368944 are subsequences.

Numbers of the form i*j*(10^k - 1)*(10^m - 1)/81 where 0 <= i, j <= 9 and k, m >= 0.

Crossrefs

Cf. A002283, A010785, A140332, A368944.

Programs

Mathematica

repQ[n_] := SameQ @@ IntegerDigits[n]; q[n_] := AnyTrue[Divisors[n], repQ[#] && repQ[n/#] &]; q[0] = True; Select[Range[0, 333], q] (* Amiram Eldar, Jan 12 2024 *)

Python

from itertools import count, takewhile
def repdigits():
    yield 0
    yield from ((10**d-1)//9*i for d in count(1) for i in range(1, 10))
def aupto(LIMIT): # use LIMIT = 10**34 for 10K+-term b-file
    s, R = set(), list(takewhile(lambda x:x<=LIMIT, repdigits()))
    for i, r1 in enumerate(R):
        for r2 in R[i:]:
            p = r1*r2
            if p > LIMIT: break
            s.add(p)
    return sorted(s)
print(aupto(333)) # Michael S. Branicky, Jan 10 2024

Formula

a(n) = A140332(n) for n <= 46.