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

1,1

Links

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A046328, A046376.

Sequence in context: A035134 A075799 A046392 * A123017 A264043 A056821

Adjacent sequences: A046405 A046406 A046407 * A046409 A046410 A046411

Keyword

nonn,base

Author

Patrick De Geest, Jun 15 1998

Extensions

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

Status

approved