A181412 -id:A181412 - 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

A179889 Triangular numbers whose reverse is a square (possibly with fewer digits).

Original entry on oeis.org

1, 10, 630, 52650, 165600, 986310, 9446031, 9485190, 10693000, 1270004401, 14214075921, 140884670790, 1809702709101, 4614899724711, 6766532724546, 9802814901400, 10210140486640, 14287075542460, 52657436563056, 98855178542676

Offset: 1

Harvey P. Dale, Jan 30 2011

			9446031 is triangular and 1306449 is a square.

Giovanni Resta, Table of n, a(n) for n = 1..36 (terms < 2*10^24)

A variant of A066703. Cf. A069673, A181412, A066528.

trnos=Accumulate[Range[14070000]];
sqnoQ[n_]:=IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[n]]]]]
Select[trnos,sqnoQ]  (* Harvey P. Dale, Jan 31 2011 *)

More terms from Harvey P. Dale, Jan 31 2011

A066702 Square numbers whose reverse is triangular with the same number of digits.

Original entry on oeis.org

0, 1, 1306449, 1044000721, 12957041241, 1019072079081, 1174279984164, 6454272356676, 65036563475625, 67624587155889, 123826990849454025, 170448128872993657764, 19198191503444720114404

Offset: 1

Erich Friedman, Jan 14 2002

The sequence of corresponding triangular numbers is A066703. - Robert G. Wilson v, Jan 31 2011

			9446031 is triangular and 1306449 is a square.

Cf. A066703, A181412. - Harvey P. Dale, Jan 30 2011

lst = {0}; For[i = 1, i > 0, i++, s = i^2; t = FromDigits@ Reverse@ IntegerDigits@ s; If[ IntegerQ@ Sqrt[8 t + 1] && Mod[s, 10] > 0, AppendTo[lst, s]; Print@ lst]]

a(12)-a(13) from and offset corrected by Giovanni Resta, Jun 20 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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A179889 Triangular numbers whose reverse is a square (possibly with fewer digits).

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A066702 Square numbers whose reverse is triangular with the same number of digits.

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Mathematica

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