A225739 Palindromic squares whose sum of digits is also a palindromic square.

1, 4, 9, 121, 10201, 12321, 1002001, 100020001, 102030201, 10000200001, 1000002000001, 1002003002001, 100000020000001, 10000000200000001, 10002000300020001, 1000000002000000001, 100000000020000000001, 100002000030000200001

Offset: 1

Author

Jayanta Basu, May 14 2013

Keywords

• nonn
• base

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

Examples

			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.
		

Crossrefs

Subsequence of A002779.

Programs

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

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

Formula

a(n) < 32^n. - Charles R Greathouse IV, May 14 2013

Extensions

a(13)-a(18) from Charles R Greathouse IV, May 14 2013