A035125 -id:A035125 - cp's OEIS frontend

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

Patrick De Geest, Nov 15 1998

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

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

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.

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

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

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

A035123 Roots of 'non-palindromic squares remaining square when written backwards'.

Original entry on oeis.org

12, 13, 21, 31, 33, 99, 102, 103, 112, 113, 122, 201, 211, 221, 301, 311, 1002, 1003, 1011, 1012, 1013, 1021, 1022, 1031, 1101, 1102, 1103, 1112, 1113, 1121, 1122, 1201, 1202, 1211, 1212, 1301, 2001, 2011, 2012, 2021, 2022, 2101, 2102, 2111, 2121

Offset: 1

Patrick De Geest, Nov 15 1998

Those with trailing zeros are excluded.

Union of ordered entries of A106323 and A106324. - Lekraj Beedassy, May 02 2005

			1212^2 = 1468944 -> 4498641 = 2121^2.

Jon E. Schoenfield, Table of n, a(n) for n = 1..8448 (first 798 terms from Seiichi Manyama; all terms < 10^10)
Patrick De Geest, Palindromic Squares in bases 2 to 17
Eric Weisstein's World of Mathematics, Square Number

Cf. A035090, A035125.

r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Select[Range[2200], Mod[#, 10] != 0 && IntegerQ[Sqrt[r[#^2]]] && r[#^2] != #^2 &] (* Jean-François Alcover, Mar 08 2011 *)

A035124 Nonpalindromic cubes remaining cubic which written backwards: take the cube root of n, reverse its digits, cube that and the result is n with its digits reversed.

Original entry on oeis.org

1033364331, 1334633301, 1003303631331, 1331363033001, 1000330036301331, 1003033061330301, 1003333697667631, 1030331603303001, 1030637669664331, 1331036300330001, 1334669667360301, 1367667963333001, 1000033000363001331, 1000303030604030301, 1000333036964367631

Offset: 1

Patrick De Geest, Nov 15 1998

Cubes with trailing zeros are excluded.

			1011^3 = 1033364331 -> 1334633301 = 1101^3.
1003333697667631 is included because its cube root, 100111, when reversed (i.e., 111001) and cubed yields 1367667963333001.

P. De Geest, Palindromic Cubes
Eric Weisstein's World of Mathematics, Cubic Number
Index entry for sequences related to reversing digits of squares

Cf. A035090, A035125, A064021, A319389.

isok(n) = {if (ispower(n, 3, &k), dn = digits(n); if (Vecrev(dn) != dn, dk = Vecrev(digits(k)); rk = subst(Pol(dk, x), x, 10); digits(rk^3) == Vecrev(dn);););} \\ Michel Marcus, Oct 04 2015

More terms from Seiichi Manyama, Sep 18 2018

A035122 Roots of 'squares remaining square when written backwards'.

Original entry on oeis.org

1, 2, 3, 11, 12, 13, 21, 22, 26, 31, 33, 99, 101, 102, 103, 111, 112, 113, 121, 122, 201, 202, 211, 212, 221, 264, 301, 307, 311, 836, 1001, 1002, 1003, 1011, 1012, 1013, 1021, 1022, 1031, 1101, 1102, 1103, 1111, 1112, 1113, 1121, 1122, 1201, 1202, 1211

Offset: 1

Patrick De Geest, Nov 15 1998

Numbers with trailing zeros are excluded.

			99^2 = 9801 -> 1089 = 33^2.

Eric Weisstein's World of Mathematics, Square Number
Index entry for sequences related to reversing digits of squares

Cf. A033294, A035125.

Select[Range[10000], IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[ #^2]]]]] &] (* and then delete terms ending with 0 - N. J. A. Sloane, Jul 08 2011 *)
Sqrt[Select[Range[2000]^2, Mod[#, 10]!=0&&IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[#]]]]]&]] (* Vincenzo Librandi, Sep 22 2015 *)

a(n) = sqrt(A033294(n)). - Michel Marcus, Sep 22 2015

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

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A035123 Roots of 'non-palindromic squares remaining square when written backwards'.

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A035124 Nonpalindromic cubes remaining cubic which written backwards: take the cube root of n, reverse its digits, cube that and the result is n with its digits reversed.

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A035122 Roots of 'squares remaining square when written backwards'.

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