cp's OEIS Frontend

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.

%I A346290 #17 Aug 21 2021 22:37:49
%S A346290 24,26,28,36,39,42,46,48,62,63,64,68,69,82,84,86,93,96,132,143,144,
%T A346290 154,156,165,168,169,176,187,198,204,206,208,224,226,228,231,244,246,
%U A346290 248,252,253,264,266,268,273,275,276,284,286,288,294,297,299,306,309
%N 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.
%C A346290 This sequence looks like A346133 but reversed products are here included.
%e A346290 a(1) = 24 = 2 * 12 and 2 * 21 = 42 (which is 24 reversed);
%e A346290 a(2) = 26 = 2 * 13 and 2 * 31 = 62 (which is 26 reversed);
%e A346290 a(3) = 28 = 2 * 14 and 2 * 41 = 82 (which is 28 reversed);
%e A346290 a(4) = 36 = 3 * 12 and 3 * 21 = 63 (which is 36 reversed); etc.
%t A346290 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 *)
%o A346290 (Python)
%o A346290 from sympy import divisors
%o A346290 def rev(n): return int(str(n)[::-1])
%o A346290 def ok(n):
%o A346290     divs = divisors(n)
%o A346290     for a in divs[1:(len(divs)+1)//2]:
%o A346290         b = n // a
%o A346290         reva, revb, revn = rev(a), rev(b), rev(n)
%o A346290         if a%10 == 0 or b%10 == 0: continue
%o A346290         if (reva != a or revb != b) and revn == reva * revb: return True
%o A346290     return False
%o A346290 print(list(filter(ok, range(310)))) # _Michael S. Branicky_, Jul 13 2021
%Y A346290 Cf. A066531, A346133.
%K A346290 nonn,base
%O A346290 1,1
%A A346290 _Eric Angelini_ and _Carole Dubois_, Jul 13 2021