This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(5)=94605 has 5 distinct factors 3 * 5 * 7 * 17 * 53 and 3571753 is palindromic.
E.g., 14432823441 = 3 * 3 * 281 * 313 * 18233 -> 3328131318233 is palindromic.
d[n_] := IntegerDigits[n]; co[n_, k_] := Nest[Flatten[d[{#, n}]] &, n, k - 1]; t = {}; Do[If[! PrimeQ[n] && Reverse[x = d[n]] == x && Reverse[y = Flatten[d[co @@@ FactorInteger[n]]]] == y, AppendTo[t, n]], {n, 2, 10^7}]; t (* Jayanta Basu, Jun 24 2013 *)
E.g., 429 = 3 * 11 * 13 -> 31113 is palindromic.
Select[Range[6210], ! PrimeQ[#] && SquareFreeQ[#] && Reverse[x = Flatten[IntegerDigits[First /@ FactorInteger[#]]]] == x &] (* Jayanta Basu, Jun 24 2013 *) Select[Range[6500],!PrimeQ[#]&&SquareFreeQ[#]&&PalindromeQ[ FromDigits[ Flatten[ IntegerDigits/@ FactorInteger[#][[All,1]]]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 25 2020 *)
3899 = 7 * 557 -> 7557 is palindromic.
d[n_] := IntegerDigits[n]; co[n_, k_] := Nest[Flatten[d[{#, n}]] &, n, k - 1]; Select[Range[8520], PrimeOmega[#] == 2 && Reverse[x = Flatten[d[co @@@ FactorInteger[#]]]] == x &] (* Jayanta Basu, Jun 26 2013 *)
Select[Range[9000],PrimeOmega[#]==2&&PalindromeQ[FromDigits[ Flatten[ IntegerDigits/@FactorInteger[#][[All,1]]]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 19 2020 *)
14133 = 3 * 7 * 673 -> 37673 is palindromic.
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
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 *)
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
164145 = 3 * 5 * 31 * 353 -> 3531353 is palindromic.
pal4Q[n_]:=Module[{ds=Flatten[IntegerDigits/@(Table[First[#],{Last[ #]}]&/@ FactorInteger[n])]},PrimeOmega[n]==4&&ds==Reverse[ds]]; Select[ Range[190000],pal4Q] (* Harvey P. Dale, Nov 12 2011 *)
320385 = 3 * 5 * 13 * 31 * 53 -> 35133153 is palindromic.
3398759 = 7 * 13 * 13 * 13 * 13 * 17 -> 71313131317 is palindromic.
17998875 = 3 * 3 * 3 * 5 * 5 * 5 * 5333 -> 3335555333 is palindromic.
2484375 = 3 * 5 * 5 * 5 * 5 * 5 * 5 * 53 -> 355555553 is palindromic.
For[n=2,n<1000000,n++,factors=FactorInteger[n]; If[Total[Transpose[factors][[2]]]!=8,Continue[]];digits={}; For[i=1,i<=Length[factors],i++, digits=Join[digits, Flatten[Table[IntegerDigits[factors[[i,1]]],{factors[[i,2]]}]]];]; If[digits==Reverse[digits],Print[n]];]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 17 2006 *)
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