A394545 Base 10 palindromes greater than 1 such that division by their highest prime factor also results in a palindrome.

2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 262, 282, 292, 303, 313, 333, 353, 363, 373, 383, 393, 404, 424, 454, 474, 484, 505, 515, 535, 545, 565, 606, 626, 707, 717

Offset

1,1

Comments

252 is the smallest palindrome not in this list.

Links

Table of n, a(n) for n=1..57.

Mathematics Stack Exchange, Are there infinitely many "super-palindromes"?.

Example

2 is in this list since its highest prime factor is 2. 2/2=1 is a palindrome.
22 is in this list since its highest prime factor is 2. 22/2=11 is a palindrome.
252 is not in this list since its highest prime factor is 7. 252/7=36 is not a palindrome.

Mathematica

q[k_] := PalindromeQ[k] && PalindromeQ[k/FactorInteger[k][[-1, 1]]]; Select[Range[2, 720], q] (* Amiram Eldar, Mar 24 2026 *)

Prog

(Python)
from itertools import islice
from sympy import primefactors
from oeis_sequences.OEISsequences import is_pal, pal10_gen
def A394545_gen(): # generator of terms
    return filter(lambda m: m>1 and is_pal(m//max(primefactors(m))), pal10_gen())
A394545_list = list(islice(A394545_gen(), 57)) # Chai Wah Wu, Mar 29 2026

Crossrefs

Cf. A002113, A394544, A394546.

Sequence in context: A335779 A240601 A324988 * A276354 A084982 A110785

Adjacent sequences: A394542 A394543 A394544 * A394546 A394547 A394548

Keyword

nonn,easy,base

Author

Robin Jones, Mar 24 2026

Status

approved