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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

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

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Last modified November 20 12:13 EST 2019. Contains 329335 sequences. (Running on oeis4.)