A048343 Number of palindromes of the form k*rev(k), where k is a non-palindromic n-digit number and rev(k) = A004086(k) is the digit reversal of k.

0, 1, 3, 10, 19, 44, 86, 171, 308, 551, 920, 1519, 2419

Offset

1,3

Comments

Numbers that have more than one such representation are counted only once. The smallest such number is 122343595343221 = 10110121*12101101 = 11002111*11120011. - Pontus von Brömssen, Mar 06 2026

Links

Table of n, a(n) for n=1..13.

Patrick De Geest, Palindromic Products of Non Palindromic Integers and their Reversals.

Example

E.g., the a(3) = 3 solutions for 3-digit numbers are: 102 * 201 = 20502; 112 * 211 = 23632; 122 * 221 = 26962.

Prog

(Python)
def A048343(n):
    y, plist = 0, []
    for i in range(10**(n-1), 10**n):
        s1 = str(i)
        s2 = s1[::-1]
        if s1 != s2:
            p = i*int(s2)
            if not p in plist:
                sp = str(p)
                if sp == sp[::-1]:
                    plist.append(p)
                    y += 1
    return y # Chai Wah Wu, Sep 05 2014

Crossrefs

Cf. A004086, A048344.

Sequence in context: A160002 A294421 A027177 * A056789 A174476 A098645

Adjacent sequences: A048340 A048341 A048342 * A048344 A048345 A048346

Keyword

nonn,base,more

Author

Patrick De Geest, Feb 15 1999

Extensions

a(7)-a(9) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 18 2006

Offset changed and a(10)-a(11) added by Lars Blomberg, Nov 25 2011

a(12) from Chai Wah Wu, Feb 21 2026

a(13) from Chai Wah Wu, Mar 05 2026

Name edited by Pontus von Brömssen, Mar 06 2026

Status

approved