A046408 - OEIS

%I #31 Sep 11 2022 09:31:47

%S 6,22,33,55,77,202,262,303,393,505,626,707,939,1111,1441,1661,1991,

%T 3443,3883,7997,13231,15251,18281,19291,20602,22622,22822,24842,26662,

%U 28682,30903,31613,33933,35653,37673,38683,39993,60206,60406,60806,62026,64646,64846

%N Palindromes with exactly 2 distinct palindromic prime factors.

%H Michael S. Branicky, <a href="/A046408/b046408.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Python)

%o from sympy import factorint

%o from itertools import product

%o def ispal(n): s = str(n); return s == s[::-1]

%o def pals(d, base=10): # all d-digit palindromes

%o     digits = "".join(str(i) for i in range(base))

%o     for p in product(digits, repeat=d//2):

%o         if d > 1 and p[0] == "0": continue

%o         left = "".join(p); right = left[::-1]

%o         for mid in [[""], digits][d%2]: yield int(left + mid + right)

%o def ok(pal):

%o     f = factorint(pal)

%o     return len(f) == 2 and sum(f.values()) == 2 and all(ispal(p) for p in f)

%o 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 (PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d) \\ A002113

%o 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 Cf. A046328, A046376.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Jun 15 1998

%E a(41) and beyond from _Michael S. Branicky_, Jun 22 2021