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

%I A368944 #18 Jan 12 2024 22:24:31
%S A368944 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,121,222,242,333,
%T A368944 363,444,484,555,616,666,777,888,999,1111,1221,2222,2442,3333,3663,
%U A368944 4444,4884,5445,5555,6666,6776,7777,8888,9999,11111,12221,12321,22222,24442,24642
%N A368944 Palindromes in base 10 that are the product of two repdigit numbers.
%C A368944 A002113 and A368955 are supersequences.
%C A368944 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.
%e A368944 121 = 11*11, 222 = 111*2, 242 = 22*11, ...
%t A368944 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 *)
%o A368944 (Python)
%o A368944 from itertools import count, takewhile
%o A368944 def ispal(n): return (s:=str(n)) == s[::-1]
%o A368944 def repdigits():
%o A368944     yield 0
%o A368944     yield from ((10**d-1)//9*i for d in count(1) for i in range(1, 10))
%o A368944 def aupto(LIMIT): # use LIMIT = 10**450 for 10K+-term b-file
%o A368944     s, R = set(), list(takewhile(lambda x:x<=LIMIT, repdigits()))
%o A368944     for i, r1 in enumerate(R):
%o A368944         for r2 in R[i:]:
%o A368944             p = r1*r2
%o A368944             if p > LIMIT: break
%o A368944             if ispal(p): s.add(p)
%o A368944     return sorted(s)
%o A368944 print(aupto(3*10**4)) # _Michael S. Branicky_, Jan 10 2024
%Y A368944 Cf. A002113, A002283, A010785 (subsequence), A368955.
%K A368944 nonn,base,easy
%O A368944 1,3
%A A368944 _Stefano Spezia_, Jan 10 2024