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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified April 5 20:14 EDT 2020. Contains 333260 sequences. (Running on oeis4.)