A046408 Palindromes with exactly 2 distinct palindromic prime factors.

6, 22, 33, 55, 77, 202, 262, 303, 393, 505, 626, 707, 939, 1111, 1441, 1661, 1991, 3443, 3883, 7997, 13231, 15251, 18281, 19291, 20602, 22622, 22822, 24842, 26662, 28682, 30903, 31613, 33933, 35653, 37673, 38683, 39993, 60206, 60406, 60806, 62026, 64646, 64846

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046328, A046376.

Programs

Mathematica

Select[Range[65000],PalindromeQ[#]&&Total[Boole[PalindromeQ/@ FactorInteger[ #][[All,1]]]]==2&&PrimeOmega[#]==2&] (* Harvey P. Dale, Aug 07 2021 *)

PARI

ispal(n) = my(d=digits(n)); d == Vecrev(d) \\ A002113
for(k=1, 1e5, if(ispal(k)&&bigomega(k)==2,a=divisors(k); if(#a==4&&ispal(a[2])&&ispal(a[3]), print1(k,", ")))) \\ Alexandru Petrescu, Aug 14 2022

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):
    f = factorint(pal)
    return len(f) == 2 and sum(f.values()) == 2 and all(ispal(p) for p in f)
print(list(filter(ok, (p for d in range(1, 6) for p in pals(d) if ok(p))))) # Michael S. Branicky, Jun 22 2021

Extensions

a(41) and beyond from Michael S. Branicky, Jun 22 2021