|
%I #18 May 14 2013 21:14:52
%S 1,4,9,121,10201,12321,1002001,100020001,102030201,10000200001,
%T 1000002000001,1002003002001,100000020000001,10000000200000001,
%U 10002000300020001,1000000002000000001,100000000020000000001,100002000030000200001
%N Palindromic squares whose sum of digits is also a palindromic square.
%C Are there finitely many terms not of the form (10^n+1)^2 or (100^n+10^n+1)^2? I haven't found any. - _Charles R Greathouse IV_, May 14 2013
%F a(n) < 32^n. - _Charles R Greathouse IV_, May 14 2013
%e 12321 is included because it is a palindromic square and 1+2+3+2+1=9 is also a palindromic square.
%e 5265533355625 is not included because although it is a palindromic square its sum of digits, 55, is not.
%t id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[id[n]]==id[n]; t={}; Do[If[palQ[x=n^2] && palQ[y=Total[id[x]]] && IntegerQ[Sqrt[y]], AppendTo[t,x]],{n,1.2*10^6}]; t
%o (PARI) ispal(n)=my(v=digits(n));for(i=1,#v\2,if(v[i]!=v[#v+1-i],return(0)));1
%o for(n=1,1e6,s=sumdigits(n^2); issquare(s) && ispal(s) && ispal(n^2) && print1(n^2", ")) \\ _Charles R Greathouse IV_, May 14 2013
%Y Subsequence of A002779.
%K nonn,base
%O 1,2
%A _Jayanta Basu_, May 14 2013
%E a(13)-a(18) from _Charles R Greathouse IV_, May 14 2013
| 