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

1,1

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

P. De Geest, Palindromic Squares

Index entry for sequences related to reversing digits of squares

Formula

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

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 *)

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.

Sequence in context: A085426 A034289 A062917 * A064021 A156316 A323614

Adjacent sequences: A035087 A035088 A035089 * A035091 A035092 A035093

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 1998

Status

approved