A046338 Palindromes > 0 with an even number of prime factors (counted with multiplicity).

1, 4, 6, 9, 22, 33, 55, 77, 88, 111, 121, 141, 161, 202, 232, 262, 303, 323, 393, 414, 424, 444, 454, 484, 505, 515, 525, 535, 545, 565, 585, 626, 636, 666, 676, 686, 707, 717, 737, 767, 808, 818, 838, 858, 868, 878, 898, 939, 949, 959, 979, 989, 999, 1111, 1441

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..17500 (terms 1..10000 from John Cerkan)

Crossrefs

Cf. A028260, A046337.

Programs

Mathematica

Select[Range[1500],PalindromeQ[#]&&EvenQ[PrimeOmega[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 01 2020 *)

Python

from sympy import factorint
from itertools import product
def ispal(n): s = str(n); return s == s[::-1]
def pals(d, base=10): # all d-digit palindromes
    digits = "".join(str(i) for i in range(base))
    for p in product(digits, repeat=d//2):
        if d > 1 and p[0] == "0": continue
        left = "".join(p); right = left[::-1]
        for mid in [[""], digits][d%2]: yield int(left + mid + right)
def ok(pal): return sum(factorint(pal).values())%2 == 0
print(list(filter(ok, (p for d in range(1, 5) for p in pals(d) if ok(p))))) # Michael S. Branicky, Aug 14 2022

Extensions

Corrected by Harvey P. Dale, Jan 01 2020