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.

24, 26, 28, 36, 39, 46, 48, 68, 69, 132, 143, 144, 154, 156, 165, 168, 169, 176, 187, 198, 204, 206, 208, 224, 226, 228, 244, 246, 248, 252, 253, 264, 266, 268, 273, 275, 276, 284, 286, 288, 294, 297, 299, 306, 309, 336, 339, 366, 369, 374, 384, 385, 396, 399

Offset: 1

Author

Eric Angelini and Carole Dubois, Jul 05 2021

Keywords

• base
• nonn

Examples

			a(1) = 24 = 2 * 12 and 2 * 21 = 42 (which is 24 reversed);
a(2) = 26 = 2 * 13 and 2 * 31 = 62 (which is 26 reversed);
a(3) = 28 = 2 * 14 and 2 * 41 = 82 (which is 28 reversed);
a(4) = 36 = 3 * 12 and 3 * 21 = 63 (which is 36 reversed); etc.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A066531.

Programs

Mathematica

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 *)

Python

from sympy import divisors
def rev(n): return int(str(n)[::-1])
def ok(n):
    divs = divisors(n)
    for a in divs[1:(len(divs)+1)//2]:
        b = n // a
        reva, revb, revn = rev(a), rev(b), rev(n)
        if revn < n or a%10 == 0 or b%10 == 0: continue
        if (reva != a or revb != b) and revn == reva * revb: return True
    return False
print(list(filter(ok, range(400)))) # Michael S. Branicky, Jul 06 2021