A129623 - OEIS

%I #22 Sep 30 2024 16:24:59

%S 252,403,574,736,765,976,1008,1207,1300,1458,1462,1612,1729,1855,1944,

%T 2268,2296,2430,2668,2701,2944,3154,3478,3627,3640,4032,4275,4606,

%U 4930,5092,5605,5848,6624,6786,7663,8722,20502,23632,26962,30492,31003,34222

%N Numbers which are the product of a non-palindrome and its reversal, where leading zeros are not allowed.

%C The smallest square in this sequence is 63504 = 252*252 = 144*441.

%H Michael S. Branicky, <a href="/A129623/b129623.txt">Table of n, a(n) for n = 1..11195</a> (terms < 10^9)

%e 252 = 12*21.

%t Take[Union[ Transpose[ Select[Table[{n, n* FromDigits[Reverse[IntegerDigits[n]]]}, {n, 1000}], Mod[ #[[1]], 10] != 0 && #[[1]] != FromDigits[Reverse[IntegerDigits[ #[[1]]]]] &]][[2]]], 100]

%t upto2ndigits@n_ := Union@(If[(i = IntegerReverse@#) > #, i*#, Nothing] & /@Range@(10^n - 1)); upto2ndigits@3 (* _Hans Rudolf Widmer_, Sep 06 2024 *)

%o (Python)

%o from sympy import divisors

%o def ok(n): return any(n==d*int(s[::-1]) for d in divisors(n)[1:-1] if (s:=str(d))!=s[::-1] and s[-1]!="0")

%o print([k for k in range(36000) if ok(k)]) # _Michael S. Branicky_, Sep 07 2024

%o (Python) # instantly generates 44185 terms with n = 5

%o def aupto2ndigits(n): return(sorted(set(i*int(s[::-1]) for i in range(12, 10**n) if i%10 != 0 and (s:=str(i)) != s[::-1])))

%o print(aupto2ndigits(2))

%o # _Michael S. Branicky_, Sep 08 2024 after _Hans Rudolf Widmer_

%Y Cf. A072443, A076750.

%K base,nonn

%O 1,1

%A _Tanya Khovanova_, May 30 2007

%E Offset corrected by _Stefano Spezia_, Sep 07 2024