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

1,3

Comments

Contains A002778. - Robert Israel, Sep 20 2015

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

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Index entry for sequences related to reversing digits of squares

Formula

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

Example

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

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]]]]] &]

Prog

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

Crossrefs

Cf. A002778, A002942.

Cf. A061457 (squares).

Sequence in context: A371030 A276326 A007090 * A069967 A061909 A345358

Adjacent sequences: A102856 A102857 A102858 * A102860 A102861 A102862

Keyword

base,easy,nonn

Author

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

Extensions

0 inserted by Jon E. Schoenfield, Sep 20 2015

Status

approved