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