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A046408 Palindromes with exactly 2 distinct palindromic prime factors.

%I A046408 #31 Sep 11 2022 09:31:47
%S A046408 6,22,33,55,77,202,262,303,393,505,626,707,939,1111,1441,1661,1991,
%T A046408 3443,3883,7997,13231,15251,18281,19291,20602,22622,22822,24842,26662,
%U A046408 28682,30903,31613,33933,35653,37673,38683,39993,60206,60406,60806,62026,64646,64846
%N A046408 Palindromes with exactly 2 distinct palindromic prime factors.
%H A046408 Michael S. Branicky, <a href="/A046408/b046408.txt">Table of n, a(n) for n = 1..10000</a>
%t A046408 Select[Range[65000],PalindromeQ[#]&&Total[Boole[PalindromeQ/@ FactorInteger[ #][[All,1]]]]==2&&PrimeOmega[#]==2&] (* _Harvey P. Dale_, Aug 07 2021 *)
%o A046408 (Python)
%o A046408 from sympy import factorint
%o A046408 from itertools import product
%o A046408 def ispal(n): s = str(n); return s == s[::-1]
%o A046408 def pals(d, base=10): # all d-digit palindromes
%o A046408     digits = "".join(str(i) for i in range(base))
%o A046408     for p in product(digits, repeat=d//2):
%o A046408         if d > 1 and p[0] == "0": continue
%o A046408         left = "".join(p); right = left[::-1]
%o A046408         for mid in [[""], digits][d%2]: yield int(left + mid + right)
%o A046408 def ok(pal):
%o A046408     f = factorint(pal)
%o A046408     return len(f) == 2 and sum(f.values()) == 2 and all(ispal(p) for p in f)
%o A046408 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
%o A046408 (PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d) \\ A002113
%o A046408 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
%Y A046408 Cf. A046328, A046376.
%K A046408 nonn,base
%O A046408 1,1
%A A046408 _Patrick De Geest_, Jun 15 1998
%E A046408 a(41) and beyond from _Michael S. Branicky_, Jun 22 2021