OFFSET
1,2
COMMENTS
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
FORMULA
a(n) < 32^n. - Charles R Greathouse IV, May 14 2013
EXAMPLE
12321 is included because it is a palindromic square and 1+2+3+2+1=9 is also a palindromic square.
5265533355625 is not included because although it is a palindromic square its sum of digits, 55, is not.
MATHEMATICA
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
PROG
(PARI) ispal(n)=my(v=digits(n)); for(i=1, #v\2, if(v[i]!=v[#v+1-i], return(0))); 1
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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jayanta Basu, May 14 2013
EXTENSIONS
a(13)-a(18) from Charles R Greathouse IV, May 14 2013
STATUS
approved