A129623 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

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

EXAMPLE

252 = 12*21.

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 *)

PROG

(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

CROSSREFS

Cf. A072443, A076750.