A346290 Numbers k = s * t such that reverse(k) = reverse(s) * reverse(t) where reverse(k) is k with its digits reversed. A single-digit number is its own reversal and neither s nor t has a leading zero. No pair (s, t) has both s and t palindromic or single-digit.

24, 26, 28, 36, 39, 42, 46, 48, 62, 63, 64, 68, 69, 82, 84, 86, 93, 96, 132, 143, 144, 154, 156, 165, 168, 169, 176, 187, 198, 204, 206, 208, 224, 226, 228, 231, 244, 246, 248, 252, 253, 264, 266, 268, 273, 275, 276, 284, 286, 288, 294, 297, 299, 306, 309

Offset

1,1

Comments

This sequence looks like A346133 but reversed products are here included.

Links

Table of n, a(n) for n=1..55.

Example

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.

Mathematica

q[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, 300], q] (* Amiram Eldar, Jul 13 2021 *)

Prog

(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 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(310)))) # Michael S. Branicky, Jul 13 2021

Crossrefs

Cf. A066531, A346133.

Sequence in context: A042198 A002924 A241042 * A097376 A346133 A079720

Adjacent sequences: A346287 A346288 A346289 * A346291 A346292 A346293

Keyword

nonn,base

Author

Eric Angelini and Carole Dubois, Jul 13 2021

Status

approved