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A046365 Composite palindromes whose sum of prime factors is prime (counted with multiplicity).

%I A046365 #18 Jun 22 2021 11:35:34
%S A046365 6,22,88,99,202,252,333,414,424,454,464,595,686,747,777,808,838,848,
%T A046365 858,909,1001,1551,1771,2442,3553,4114,5335,5775,6336,6996,8008,8228,
%U A046365 9009,9559,9669,9889,12121,14241,16261,16761,17171,18081,18381,20102,20602,21012
%N A046365 Composite palindromes whose sum of prime factors is prime (counted with multiplicity).
%H A046365 Michael S. Branicky, <a href="/A046365/b046365.txt">Table of n, a(n) for n = 1..10000</a>
%F A046365 A046363 INTERSECT A002113. - _R. J. Mathar_, Sep 09 2015
%t A046365 Select[Range[20125], !PrimeQ[#] && Reverse[x=IntegerDigits[#]] == x && PrimeQ[Total[Times@@@FactorInteger[#]]]&] (* _Jayanta Basu_, May 29 2013 *)
%o A046365 (Python)
%o A046365 from itertools import product
%o A046365 from sympy import factorint, isprime
%o A046365 def pals(d, base=10): # all d-digit palindromes
%o A046365     digits = "".join(str(i) for i in range(base))
%o A046365     for p in product(digits, repeat=d//2):
%o A046365         if d > 1 and p[0] == "0": continue
%o A046365         left = "".join(p); right = left[::-1]
%o A046365         for mid in [[""], digits][d%2]: yield int(left + mid + right)
%o A046365 def ok(pal):
%o A046365     f = factorint(pal); return len(f)>1 and isprime(sum(p*f[p] for p in f))
%o A046365 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
%Y A046365 Cf. A046363, A046364.
%K A046365 nonn,base
%O A046365 1,1
%A A046365 _Patrick De Geest_, Jun 15 1998
%E A046365 a(45) and beyond from _Michael S. Branicky_, Jun 22 2021