

A225739


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


1



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



