A046452 Numbers that are the product of 3 prime factors whose concatenation is a palindrome.

8, 27, 125, 343, 429, 507, 795, 1309, 1331, 1533, 1547, 1587, 2023, 2097, 3633, 3729, 3897, 5289, 5295, 5547, 6597, 7833, 8029, 8427, 9583, 9795, 12207, 12795, 13489, 13573, 14133, 14147, 14295, 15463, 15549, 15987, 16233, 17295, 20667, 22139, 28273, 28609, 28847, 28951

Offset: 1

Author

Patrick De Geest, Jul 15 1998

Keywords

• nonn
• base

Comments

Sequence is the intersection of A046447 and A014612 without the initial term. - Charles R Greathouse IV, Apr 23 2010

Apart from a(1) all terms are odd. Apart from a(3) 5 divides a(n) if and only if 15 divides a(n). - Charles R Greathouse IV, Jan 04 2013

Examples

			14133 = 3 * 7 * 673 -> 37673 is palindromic.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2292

Crossrefs

Cf. A046447.

Programs

Maple

Nmax:= 10000; # to get all a(n) <= Nmax
R:= {8}:
for i from 2 do
   a:= ithprime(i);
   if a^3 > Nmax then break end if;
   m:= length(a); tm:= 10^m;
   al:= convert(a,base,10);
   ar:= add(10^(m-k)*al[k],k=1..m);
   for j from i  do
     b:= ithprime(j);
     if a*b^2 > Nmax then break end if;
     bl:= convert(b,base,10);
     k0:= ceil((b-ar)/tm);
     for k from k0 do
       c:= ar + k*tm;
       if a*b*c > Nmax then break end if;
       if not isprime(c) then next end if;
       L:= [op(convert(c,base,10)),op(bl),op(al)];
       if ListTools:-Reverse(L)=L then
         R:= R union {a*b*c}
       end if;
     end do
   end do
end do:
R;  # Robert Israel, Jan 05 2013

Mathematica

pfpQ[n_]:=Module[{c=Flatten[IntegerDigits/@Table[#[[1]],{#[[2]]}]&/@ FactorInteger[ n]]},c==Reverse[c]]; Select[Range[30000],PrimeOmega[#] == 3&&pfpQ[#]&] (* Harvey P. Dale, Jan 05 2013 *)

PARI

ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1
list(lim)=my(v=List([8]),t);forprime(p=3,lim\9, forprime(q=3,min(lim\(3*p),p), t=p*q; forprime(r=3,min(lim\t,q), if(ispal(eval(Str(r,q,p))), listput(v,t*r))))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jan 04 2013

Extensions

Missing a(16) from Charles R Greathouse IV on the advice of Harvey P. Dale, Jan 04 2013