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

1,3

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.

Links

Table of n, a(n) for n=1..64.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A002283, A010785, A140332, A368944.

Sequence in context: A084347 A051038 A140332 * A155182 A096076 A108864

Adjacent sequences: A368952 A368953 A368954 * A368956 A368957 A368958

Keyword

nonn,base,easy

Author

Stefano Spezia, Jan 10 2024

Status

approved