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A035090
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Non-palindromic squares which when written backwards remain square (and still have the same number of digits).
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12
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144, 169, 441, 961, 1089, 9801, 10404, 10609, 12544, 12769, 14884, 40401, 44521, 48841, 90601, 96721, 1004004, 1006009, 1022121, 1024144, 1026169, 1042441, 1044484, 1062961, 1212201, 1214404, 1216609, 1236544, 1238769, 1256641
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Squares with trailing zeros not included.
Sequence is infinite, since it includes, e.g., 10^(2k) + 4*10^k + 4 for all k. - Robert Israel, Sep 20 2015
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LINKS
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FORMULA
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MAPLE
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rev:= proc(n) local L, i;
L:= convert(n, base, 10);
add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
filter:= proc(n) local t;
if n mod 10 = 0 then return false fi;
t:= rev(n);
t <> n and issqr(t)
end proc:
select(filter, [seq(n^2, n=1..10^5)]); # Robert Israel, Sep 20 2015
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MATHEMATICA
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Select[Range[1200]^2, !PalindromeQ[#]&&IntegerLength[#]==IntegerLength[ IntegerReverse[ #]] && IntegerQ[Sqrt[IntegerReverse[#]]]&] (* Harvey P. Dale, Jul 19 2023 *)
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CROSSREFS
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Reversing a polytopal number gives a polytopal number:
tetrahedral to tetrahedral: A006030;
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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