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

1,2

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

Links

Table of n, a(n) for n=1..18.

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

Subsequence of A002779.

Sequence in context: A319483 A057136 A048411 * A065379 A063783 A168138

Adjacent sequences: A225736 A225737 A225738 * A225740 A225741 A225742

Keyword

nonn,base

Author

Jayanta Basu, May 14 2013

Extensions

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

Status

approved