A106324 -id:A106324 - 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 *)

A106323 Smaller of number pair whose squares are reversals of each other, with no leading zeros allowed.

Original entry on oeis.org

12, 13, 33, 102, 103, 112, 113, 122, 1002, 1003, 1011, 1012, 1013, 1021, 1022, 1031, 1102, 1103, 1112, 1113, 1121, 1122, 1202, 1212, 2012, 2022, 3168, 10002, 10003, 10011, 10012, 10013, 10021, 10022, 10031, 10102, 10103, 10111, 10112, 10113

Offset: 1

Lekraj Beedassy, Apr 29 2005

For numbers whose squares are the reversal of a(n)^2, see A106324.

			33 is in the sequence because 33^2=1089 and we have 9801=99^2. Likewise,122^2=14884 and we have 48841=221^2.

Cf. A035090; A035123.

Half of A035123.

isok(n) = {if (n % 10 == 0, return (0)); d = digits(n^2, 10); m = sum(k=0, #d-1, d[k+1]*10^(k)); if (! issquare(m), return (0)); return (n < sqrtint(m));} \\ Michel Marcus, Jul 28 2013

Corrected and extended by Joshua Zucker, May 12 2006

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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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A106323 Smaller of number pair whose squares are reversals of each other, with no leading zeros allowed.

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