A035124 -id:A035124 - 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

A035125 Roots of 'non-palindromic cubes remaining cubic when written backwards'.

Original entry on oeis.org

1011, 1101, 10011, 11001, 100011, 100101, 100111, 101001, 101011, 110001, 110101, 111001, 1000011, 1000101, 1000111, 1001011, 1001101, 1010001, 1010011, 1011001, 1100001, 1100101, 1101001, 1110001, 10000011, 10000101, 10000111, 10001001, 10001011, 10001101, 10010001

Offset: 1

Patrick De Geest, Nov 15 1998

Those with trailing zeros are excluded. Binary look is fortuitous!

			1000011^3 = 1000033000363001331 -> 1331003630003300001 = 1100001^3.

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, A035124.

More terms from Seiichi Manyama, Sep 18 2018

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.

A064021 Squares k^2 such that reverse(k)^2 = reverse(k^2), excluding squares of palindromes.

Original entry on oeis.org

144, 169, 441, 961, 10404, 10609, 12544, 12769, 14884, 40401, 44521, 48841, 90601, 96721, 1004004, 1006009, 1022121, 1024144, 1026169, 1042441, 1044484, 1062961, 1212201, 1214404, 1216609, 1236544, 1238769, 1256641, 1258884, 1442401

Offset: 1

Harvey P. Dale, Sep 18 2001

Subsequence of A035090. - M. F. Hasler, Mar 22 2011

			1026169 is included because its square root, 1013, when reversed (i.e., 3101) and squared yields 9616201.
Squares < 10 and 121 = 11^2, 484 = 22^2, ... are not in the sequence, since they are the square of a palindrome. - _M. F. Hasler_, Mar 22 2011

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 124, 127 (Rev. ed. 1997).

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 750 terms from Harry J. Smith)

Cf. A035124, A035123, A033294, A140212.

Cases[Range[2000]^2, k_ /; Mod[k, 10] != 0 && IntegerDigits[k] != Reverse[IntegerDigits[k]] && FromDigits[Reverse[IntegerDigits[Sqrt[k]]]]^2 == FromDigits[Reverse[IntegerDigits[k]]]] (* Jean-François Alcover, Mar 22 2011 *)
Select[Range[1250]^2,!PalindromeQ[Sqrt[#]]&&IntegerReverse[#] == IntegerReverse[ Sqrt[#]]^2 &&Mod[#,10]!=0&] (* Harvey P. Dale, Jul 01 2022 *)

Rev(x)= { local(d,r); r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); return(r) }
{ n=0; for (m=1, 10^9, if (m%10==0, next); x=m^2; r=Rev(x); if (r==x, next); if (r==Rev(m)^2, write("b064021.txt", n++, " ", x); if (n==750, break)) ) } \\ Harry J. Smith, Sep 06 2009

{n = A000290(k) such that A004086(A000290(k)) = A000290(A004086(k)) and k is not in A002113}. - Jonathan Vos Post, May 02 2011

a(n) = A140212(n)^2. - Giovanni Resta, Jun 22 2018

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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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A035125 Roots of 'non-palindromic cubes remaining cubic when written backwards'.

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A319389 Non-palindromic cubes.

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A064021 Squares k^2 such that reverse(k)^2 = reverse(k^2), excluding squares of palindromes.

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