A129623 Numbers which are the product of a non-palindrome and its reversal, where leading zeros are not allowed.

252, 403, 574, 736, 765, 976, 1008, 1207, 1300, 1458, 1462, 1612, 1729, 1855, 1944, 2268, 2296, 2430, 2668, 2701, 2944, 3154, 3478, 3627, 3640, 4032, 4275, 4606, 4930, 5092, 5605, 5848, 6624, 6786, 7663, 8722, 20502, 23632, 26962, 30492, 31003, 34222

Offset: 1

Author

Tanya Khovanova, May 30 2007

Keywords

• base
• nonn

Comments

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

Examples

			252 = 12*21.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..11195 (terms < 10^9)

Crossrefs

Cf. A072443, A076750.

Programs

Mathematica

Take[Union[ Transpose[ Select[Table[{n, n* FromDigits[Reverse[IntegerDigits[n]]]}, {n, 1000}], Mod[ #[[1]], 10] != 0 && #[[1]] != FromDigits[Reverse[IntegerDigits[ #[[1]]]]] &]][[2]]], 100]
upto2ndigits@n_ := Union@(If[(i = IntegerReverse@#) > #, i*#, Nothing] & /@Range@(10^n - 1)); upto2ndigits@3 (* Hans Rudolf Widmer, Sep 06 2024 *)

Python

from sympy import divisors
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")
print([k for k in range(36000) if ok(k)]) # Michael S. Branicky, Sep 07 2024

Python

# instantly generates 44185 terms with n = 5
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])))
print(aupto2ndigits(2))
# Michael S. Branicky, Sep 08 2024 after Hans Rudolf Widmer

Extensions

Offset corrected by Stefano Spezia, Sep 07 2024