A368944 Palindromes in base 10 that are the product of two repdigit numbers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 121, 222, 242, 333, 363, 444, 484, 555, 616, 666, 777, 888, 999, 1111, 1221, 2222, 2442, 3333, 3663, 4444, 4884, 5445, 5555, 6666, 6776, 7777, 8888, 9999, 11111, 12221, 12321, 22222, 24442, 24642

Offset: 1

Author

Stefano Spezia, Jan 10 2024

Keywords

• nonn
• base
• easy

Comments

A002113 and A368955 are supersequences.

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

Examples

			121 = 11*11, 222 = 111*2, 242 = 22*11, ...
		

Crossrefs

Cf. A002113, A002283, A010785 (subsequence), A368955.

Programs

Mathematica

repQ[n_] := SameQ @@ IntegerDigits[n]; q[n_] := PalindromeQ[n] && AnyTrue[Divisors[n], repQ[#] && repQ[n/#] &]; q[0] = True; Select[Range[0, 25000], q] (* Amiram Eldar, Jan 12 2024 *)

Python

from itertools import count, takewhile
def ispal(n): return (s:=str(n)) == s[::-1]
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**450 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
            if ispal(p): s.add(p)
    return sorted(s)
print(aupto(3*10**4)) # Michael S. Branicky, Jan 10 2024