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A057135
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Palindromes whose square is a palindrome; also palindromes whose sum of squares of digits is less than 10.
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9
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0, 1, 2, 3, 11, 22, 101, 111, 121, 202, 212, 1001, 1111, 2002, 10001, 10101, 10201, 11011, 11111, 11211, 20002, 20102, 100001, 101101, 110011, 111111, 200002, 1000001, 1001001, 1002001, 1010101, 1011101, 1012101, 1100011, 1101011, 1102011, 1110111, 1111111
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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121 is OK since 121^2=14641 is also a palindrome.
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MAPLE
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dmax:= 7: # to get all terms with up to dmax digits
Res:= 0, 1, 2, 3, 11, 22:
Po:= [[0], [1], [2], [3]]: Pe:= [[0, 0], [1, 1], [2, 2]]:
for d from 1 to dmax do
if d::odd then
Po:= select(t -> add(s^2, s=t) < 10, [seq(seq([i, op(t), i], t=Po), i=0..2)]);
Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1), i=1..nops(p)) fi end proc, Po))
else
Pe:= select(t -> add(s^2, s=t) < 10, [seq(seq([i, op(t), i], t=Pe), i=0..2)]);
Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1), i=1..nops(p)) fi end proc, Pe))
fi;
od:
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MATHEMATICA
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PalQ[n_] := FromDigits[Reverse[IntegerDigits[n]]] == n; t = {}; Do[
If[PalQ[n] && PalQ[n^2], AppendTo[t, n]], {n, 0, 1200000}]; t (* Jayanta Basu, May 10 2013 *)
Select[Range[0, 12*10^5], AllTrue[{#, #^2}, PalindromeQ]&](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 20 2018 *)
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PROG
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(PARI) is(n) = digits(n)==Vecrev(digits(n)) && digits(n^2)==Vecrev(digits(n^2)) \\ Felix Fröhlich, Jun 21 2017
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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