A319388 -id:A319388 - 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

A319389 Non-palindromic cubes.

Original entry on oeis.org

27, 64, 125, 216, 512, 729, 1000, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125

Offset: 1

Seiichi Manyama, Sep 18 2018

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A000578, A002113, A035124, A319388.

A319440 Squares of non-palindromic number.

Original entry on oeis.org

100, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3136, 3249, 3364, 3481, 3600, 3721, 3844

Offset: 1

Seiichi Manyama, Sep 19 2018

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000290, A002113, A029742, A319388, A319441.

[n^2: n in [0..65] | Intseq(n) ne Reverse(Intseq(n))]; // Vincenzo Librandi, Sep 19 2018

palQ[n_]:=Module[{idn=IntegerDigits[n]}, idn==Reverse[idn]]; DeleteCases[Range[10, 110],?palQ]^2 (* _Vincenzo Librandi, Sep 19 2018 *)

def A319440(n):
    def f(x): return n+x//10**((l:=len(s:=str(x)))-(k:=l+1>>1))-(int(s[k-1::-1])>x%10**k)+10**(k-1+(l&1^1))-1
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m**2 # Chai Wah Wu, Oct 28 2024

a(n) = A029742(n)^2.

A319482 a(n) = A133901(n)^2.

Original entry on oeis.org

1089, 9801, 1252409430321, 102230321074203012201, 123452123498421034321, 10223212100654001012201, 1022341432329642141232201, 1232342014329624300232321, 102234323212287620121232201, 10022030122010722200301022001, 10022230363212962214501222001

Offset: 1

Seiichi Manyama, Sep 20 2018

Non-palindromic squares in A319483.

			b(n) = reverse of a(n).
n | A133901(n) |           a(n) |           b(n) | Root of b(n) |
--+------------+----------------+----------------+--------------+
1 |        33  |          1089  |          9801  |          99  |
2 |        99  |          9801  |          1089  |          33  |
3 |   1119111  | 1252409430321  | 1230349042521  |     1109211  |

Cf. A002113, A133901, A319388, A319483.

A319570 a(n) = A284986(n)^2.

Original entry on oeis.org

1089, 9801, 10036224, 42263001, 420578064, 460875024, 12303690084, 48009630321, 92158994929, 92949985129, 1212029250084, 1230349042521, 1234147690084, 1252409430321, 4800529202121, 4800967414321, 9488660854689, 9864580668849, 102230743690084, 121200525010321

Offset: 1

Seiichi Manyama, Sep 23 2018

			b(n) = reverse of a(n).
n | A284986(n) |       a(n) |       b(n) | Root of b(n) |
--+------------+------------+------------+--------------+
1 |        33  |      1089  |      9801  |          99  |
2 |        99  |      9801  |      1089  |          33  |
3 |      3168  |  10036224  |  42263001  |        6501  |
4 |      6501  |  42263001  |  10036224  |        3168  |
5 |     20508  | 420578064  | 460875024  |       21468  |
6 |     21468  | 460875024  | 420578064  |       20508  |

Index entry for sequences related to reversing digits of squares

Cf. A284986, A319388.

cp's OEIS Frontend

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

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A319389 Non-palindromic cubes.

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A319440 Squares of non-palindromic number.

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A319482 a(n) = A133901(n)^2.

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A319570 a(n) = A284986(n)^2.

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