A102859 Numbers that when squared and written backwards give a square again.

0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 26, 30, 31, 33, 99, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 130, 200, 201, 202, 210, 211, 212, 220, 221, 260, 264, 300, 301, 307, 310, 311, 330, 836, 990, 1000, 1001, 1002, 1003, 1010, 1011, 1012, 1013, 1020

Offset: 1

Author

Sanita Kashcheyeva (sanits(AT)gmail.com), Mar 01 2005

Keywords

• base
• easy
• nonn

Comments

Contains A002778. - Robert Israel, Sep 20 2015

Squares of these terms are in A061457. - Jon E. Schoenfield, May 17 2022

Examples

			a(7)=12 belongs to the sequence since writing 12^2 = 144 backwards gives 441 = 21^2.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
• Index entry for sequences related to reversing digits of squares

Crossrefs

Cf. A002778, A002942.

Cf. A061457 (squares).

Programs

Magma

[n: n in [0..1100] | IsSquare(Seqint(Reverse(Intseq(n^2))))]; // Vincenzo Librandi, Sep 21 2015

Maple

rev:= proc(n)
  local L, Ln, i;
  L:= convert(n, base, 10);
  Ln:= nops(L);
  add(L[i]*10^(Ln-i), i=1..Ln);
end proc:
select(t -> issqr(rev(t^2)),[$0..10^5]); # Robert Israel, Sep 20 2015

Mathematica

Select[Range[1000], IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[ #^2]]]]] &]

Python

from itertools import count, islice
from sympy import integer_nthroot
def A102859_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:integer_nthroot(int(str(n**2)[::-1]),2)[1], count(max(startvalue,0)))
A102859_list = list(islice(A102859_gen(),30)) # Chai Wah Wu, Nov 18 2022

Formula

a(n) = sqrt(A061457(n)). - Jon E. Schoenfield, May 17 2022

Extensions

0 inserted by Jon E. Schoenfield, Sep 20 2015