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

6, 22, 88, 99, 202, 252, 333, 414, 424, 454, 464, 595, 686, 747, 777, 808, 838, 848, 858, 909, 1001, 1551, 1771, 2442, 3553, 4114, 5335, 5775, 6336, 6996, 8008, 8228, 9009, 9559, 9669, 9889, 12121, 14241, 16261, 16761, 17171, 18081, 18381, 20102, 20602, 21012

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. A046363, A046364.

Programs

Mathematica

Select[Range[20125], !PrimeQ[#] && Reverse[x=IntegerDigits[#]] == x && PrimeQ[Total[Times@@@FactorInteger[#]]]&] (* Jayanta Basu, May 29 2013 *)

Python

from itertools import product
from sympy import factorint, isprime
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)>1 and isprime(sum(p*f[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

Formula

A046363 INTERSECT A002113. - R. J. Mathar, Sep 09 2015

Extensions

a(45) and beyond from Michael S. Branicky, Jun 22 2021