A035090 Non-palindromic squares which when written backwards remain square (and still have the same number of digits).

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

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..798
• Patrick De Geest, Palindromic Squares in bases 2 to 17
• Index entry for sequences related to reversing digits of squares

Crossrefs

Reversing a polytopal number gives a polytopal number:

cube to cube: A035123, A035124, A035125, A002781;

square to square: A161902, A035090, A033294, A106323, A106324, A002779;

square to triangular: A181412, A066702;

tetrahedral to tetrahedral: A006030;

triangular to square: A066703, A179889;

triangular to triangular: A066528, A069673, A003098, A066569.

Cf. A319388.

Programs

Maple

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

Mathematica

Select[Range[1200]^2,!PalindromeQ[#]&&IntegerLength[#]==IntegerLength[ IntegerReverse[ #]] && IntegerQ[Sqrt[IntegerReverse[#]]]&] (* Harvey P. Dale, Jul 19 2023 *)

Formula

a(n) = A035123(n)^2. - R. J. Mathar, Jan 25 2017