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

1,3

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.

Links

Table of n, a(n) for n=1..54.

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A257054 A110784 A193408 * A346217 A353729 A227001

Adjacent sequences: A368941 A368942 A368943 * A368945 A368946 A368947

Keyword

nonn,base,easy

Author

Stefano Spezia, Jan 10 2024

Status

approved