A346290 - OEIS

%I #17 Aug 21 2021 22:37:49

%S 24,26,28,36,39,42,46,48,62,63,64,68,69,82,84,86,93,96,132,143,144,

%T 154,156,165,168,169,176,187,198,204,206,208,224,226,228,231,244,246,

%U 248,252,253,264,266,268,273,275,276,284,286,288,294,297,299,306,309

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

%e a(1) = 24 = 2 * 12 and 2 * 21 = 42 (which is 24 reversed);

%e a(2) = 26 = 2 * 13 and 2 * 31 = 62 (which is 26 reversed);

%e a(3) = 28 = 2 * 14 and 2 * 41 = 82 (which is 28 reversed);

%e a(4) = 36 = 3 * 12 and 3 * 21 = 63 (which is 36 reversed); etc.

%t 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 (Python)

%o from sympy import divisors

%o def rev(n): return int(str(n)[::-1])

%o def ok(n):

%o     divs = divisors(n)

%o     for a in divs[1:(len(divs)+1)//2]:

%o         b = n // a

%o         reva, revb, revn = rev(a), rev(b), rev(n)

%o         if a%10 == 0 or b%10 == 0: continue

%o         if (reva != a or revb != b) and revn == reva * revb: return True

%o     return False

%o print(list(filter(ok, range(310)))) # _Michael S. Branicky_, Jul 13 2021

%Y Cf. A066531, A346133.

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _Carole Dubois_, Jul 13 2021