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A346133 Numbers N = A * B such that N (reversed digits) = A (reversed digits) * B (reversed digits). A single-digit number is its own reversal and neither A nor B has a leading zero. No pair (A, B) has both A and B palindromic or simple-digit. The reversed products are not included in the sequence.

%I A346133 #28 Jun 06 2023 07:40:35
%S A346133 24,26,28,36,39,46,48,68,69,132,143,144,154,156,165,168,169,176,187,
%T A346133 198,204,206,208,224,226,228,244,246,248,252,253,264,266,268,273,275,
%U A346133 276,284,286,288,294,297,299,306,309,336,339,366,369,374,384,385,396,399
%N A346133 Numbers N = A * B such that N (reversed digits) = A (reversed digits) * B (reversed digits). A single-digit number is its own reversal and neither A nor B has a leading zero. No pair (A, B) has both A and B palindromic or simple-digit. The reversed products are not included in the sequence.
%H A346133 Michael S. Branicky, <a href="/A346133/b346133.txt">Table of n, a(n) for n = 1..10000</a>
%e A346133 a(1) = 24 = 2 * 12 and 2 * 21 = 42 (which is 24 reversed);
%e A346133 a(2) = 26 = 2 * 13 and 2 * 31 = 62 (which is 26 reversed);
%e A346133 a(3) = 28 = 2 * 14 and 2 * 41 = 82 (which is 28 reversed);
%e A346133 a(4) = 36 = 3 * 12 and 3 * 21 = 63 (which is 36 reversed); etc.
%t A346133 q[n_] := IntegerReverse[n] >= n && AnyTrue[Rest @ Take[(d = Divisors[n]), Ceiling[Length[d]/2]], (# > 9 || n/# > 9) && !Divisible[#, 10] && !Divisible[n/#, 10] && (!PalindromeQ[#] || !PalindromeQ[n/#]) && IntegerReverse[#] * IntegerReverse[n/#] == IntegerReverse[n] &]; Select[Range[2, 400], q] (* _Amiram Eldar_, Jul 07 2021 *)
%o A346133 (Python)
%o A346133 from sympy import divisors
%o A346133 def rev(n): return int(str(n)[::-1])
%o A346133 def ok(n):
%o A346133     divs = divisors(n)
%o A346133     for a in divs[1:(len(divs)+1)//2]:
%o A346133         b = n // a
%o A346133         reva, revb, revn = rev(a), rev(b), rev(n)
%o A346133         if revn < n or a%10 == 0 or b%10 == 0: continue
%o A346133         if (reva != a or revb != b) and revn == reva * revb: return True
%o A346133     return False
%o A346133 print(list(filter(ok, range(400)))) # _Michael S. Branicky_, Jul 06 2021
%Y A346133 Cf. A066531.
%K A346133 base,nonn
%O A346133 1,1
%A A346133 _Eric Angelini_ and _Carole Dubois_, Jul 05 2021