A046328 Palindromes with exactly 2 prime factors (counted with multiplicity).

4, 6, 9, 22, 33, 55, 77, 111, 121, 141, 161, 202, 262, 303, 323, 393, 454, 505, 515, 535, 545, 565, 626, 707, 717, 737, 767, 818, 838, 878, 898, 939, 949, 959, 979, 989, 1111, 1441, 1661, 1991, 3113, 3223, 3443, 3883, 7117, 7447, 7997, 9119, 9229, 9449, 10001

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 2000 terms from Zak Seidov, terms a(2001)-a(2816) from Michael De Vlieger)

Example

111 is a palindrome and 111 = 3*37. 3 and 37 are primes.

Mathematica

fQ[n_] := Block[{id = IntegerDigits[n]}, Plus @@ Last /@ FactorInteger[n] == 2 && id == Reverse[id]]; Select[ Range[ 10000], fQ[ # ] &] (* Robert G. Wilson v, Jun 06 2005 *)
Select[Range[10002], Reverse[x = IntegerDigits[#]] == x && PrimeOmega[#] == 2 &] (* Jayanta Basu, Jun 23 2013 *)
Select[Range[11000], PalindromeQ[#]&&PrimeOmega[#]==2&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 30 2018 *)

Prog

(PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d) \\ A002113
for(k=1, 1e4, if(ispal(k)&&bigomega(k)==2, print1(k, ", "))) \\ Alexandru Petrescu, Jul 07 2022
(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): return sum(factorint(pal).values()) == 2
print(list(filter(ok, (p for d in range(1, 6) for p in pals(d) if ok(p))))) # Michael S. Branicky, Aug 14 2022

Crossrefs

Cf. A046315, A046408, A108505.

Subsequence of A001358 and A046338.

Sequence in context: A046338 A118690 A084994 * A196104 A046376 A229129

Adjacent sequences: A046325 A046326 A046327 * A046329 A046330 A046331

Keyword

nonn,base

Author

Patrick De Geest, Jun 15 1998

Status

approved