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

%I A046452 #30 Oct 15 2019 12:00:23
%S A046452 8,27,125,343,429,507,795,1309,1331,1533,1547,1587,2023,2097,3633,
%T A046452 3729,3897,5289,5295,5547,6597,7833,8029,8427,9583,9795,12207,12795,
%U A046452 13489,13573,14133,14147,14295,15463,15549,15987,16233,17295,20667,22139,28273,28609,28847,28951
%N A046452 Numbers that are the product of 3 prime factors whose concatenation is a palindrome.
%C A046452 Sequence is the intersection of A046447 and A014612 without the initial term. - _Charles R Greathouse IV_, Apr 23 2010
%C A046452 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
%H A046452 Robert Israel, <a href="/A046452/b046452.txt">Table of n, a(n) for n = 1..2292</a>
%e A046452 14133 = 3 * 7 * 673 -> 37673 is palindromic.
%p A046452 Nmax:= 10000; # to get all a(n) <= Nmax
%p A046452 R:= {8}:
%p A046452 for i from 2 do
%p A046452    a:= ithprime(i);
%p A046452    if a^3 > Nmax then break end if;
%p A046452    m:= length(a); tm:= 10^m;
%p A046452    al:= convert(a,base,10);
%p A046452    ar:= add(10^(m-k)*al[k],k=1..m);
%p A046452    for j from i  do
%p A046452      b:= ithprime(j);
%p A046452      if a*b^2 > Nmax then break end if;
%p A046452      bl:= convert(b,base,10);
%p A046452      k0:= ceil((b-ar)/tm);
%p A046452      for k from k0 do
%p A046452        c:= ar + k*tm;
%p A046452        if a*b*c > Nmax then break end if;
%p A046452        if not isprime(c) then next end if;
%p A046452        L:= [op(convert(c,base,10)),op(bl),op(al)];
%p A046452        if ListTools:-Reverse(L)=L then
%p A046452          R:= R union {a*b*c}
%p A046452        end if;
%p A046452      end do
%p A046452    end do
%p A046452 end do:
%p A046452 R;  # _Robert Israel_, Jan 05 2013
%t A046452 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 *)
%o A046452 (PARI) ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1
%o A046452 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
%Y A046452 Cf. A046447.
%K A046452 nonn,base
%O A046452 1,1
%A A046452 _Patrick De Geest_, Jul 15 1998
%E A046452 Missing a(16) from _Charles R Greathouse IV_ on the advice of _Harvey P. Dale_, Jan 04 2013