A066569 -id:A066569 - 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

A069673 Nonpalindromic triangular numbers whose digit reversal is also a triangular number (possibly with fewer digits).

Original entry on oeis.org

10, 120, 153, 190, 300, 351, 630, 820, 17578, 87571, 156520, 180300, 185745, 547581, 557040, 678030, 1461195, 1851850, 5911641, 6056940, 12145056, 12517506, 16678200, 56440000, 60571521, 65054121, 157433640, 188267310, 304119453, 354911403, 1261250200

Offset: 1

Amarnath Murthy, Apr 06 2002

Giovanni Resta, Table of n, a(n) for n = 1..123 (terms < 2*10^24)

See A066528 for a different version.
Cf. A066703, A179889.
Cf. A003098, A061455, A066569.

More terms from Jason Earls, Jun 07 2002

a(27)-a(31) from Giovanni Resta, Jun 20 2015

A061455 Triangular numbers whose digit reversal is also a triangular number.

Original entry on oeis.org

0, 1, 3, 6, 10, 55, 66, 120, 153, 171, 190, 300, 351, 595, 630, 666, 820, 3003, 5995, 8778, 15051, 17578, 66066, 87571, 156520, 180300, 185745, 547581, 557040, 617716, 678030, 828828, 1269621, 1461195, 1680861, 1851850, 3544453, 5073705, 5676765, 5911641

Offset: 1

Amarnath Murthy, May 03 2001

			153 is in the sequence because (1) it is a triangular number and (2) its reversal 351 is also a triangular number.

Jon E. Schoenfield, Table of n, a(n) for n = 1..162 (terms < 10^18)

Cf. A000217, A003098, A004086, A066528, A066569, A069673.

read("transforms");
isA000217 := proc(n) issqr(1+8*n) ;end proc:
isA061455 := proc(n) isA000217(n) and isA000217(digrev(n)) ; end proc:
for n from 0 to 60000 do T := A000217(n) ; if isA061455(T) then printf("%d,", T) ; end if; end do: # R. J. Mathar, Dec 13 2010

TriangularNumberQ[k_] := If[IntegerQ[1/2 (Sqrt[1 + 8 k] - 1)], True, False]; Select[Range[0, 5676765], TriangularNumberQ[#] && TriangularNumberQ[FromDigits[Reverse[IntegerDigits[#]]]] &] (* Ant King, Dec 13 2010 *)

isok(n) = ispolygonal(n, 3) && ispolygonal(fromdigits(Vecrev(digits(n))), 3); \\ Michel Marcus, Apr 14 2019

a(n)=A000217(k) and A004086(a(n))=A000217(j) for some k and j. - R. J. Mathar, Jun 02 2006

More terms from Erich Friedman, May 08 2001

Edited by N. J. A. Sloane, Aug 13 2008 at the suggestion of R. J. Mathar

A066528 Non-palindromic triangular numbers whose reverse is a triangular number with the same number of digits.

Original entry on oeis.org

153, 351, 17578, 87571, 185745, 547581, 1461195, 5911641, 12145056, 12517506, 60571521, 65054121, 304119453, 354911403, 1775275491, 1945725771, 10246462281, 17990863516, 18226464201, 35615002605, 50620051653, 61536809971, 1222080857271, 1664224065406

Offset: 1

Erich Friedman, Jan 08 2002

			153 and 351 are both triangular.

Giovanni Resta, Table of n, a(n) for n = 1..64 (terms < 2*10^24)

See A069673 for another version.
Cf. A066703, A179889.
Cf. A003098, A061455, A066569, A069673.

dtn[L_] := Fold[10#1+#2&, 0, L]; tritest[n_] := Module[{t}, t=Floor[N[Sqrt[2n]]]; 2n==t(t+1)]; A={}; For[i=1, i>0, i++, t=i(i+1)/2; If[tritest[tt=dtn[Reverse[IntegerDigits[t]]]]&&Mod[t, 10]>0&&t=!=tt, AppendTo[A, t]; Print[A]]]

a(22)-a(24) from 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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A069673 Nonpalindromic triangular numbers whose digit reversal is also a triangular number (possibly with fewer digits).

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A061455 Triangular numbers whose digit reversal is also a triangular number.

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A066528 Non-palindromic triangular numbers whose reverse is a triangular number with the same number of digits.

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