A061457 Squares whose reversal is also a square.

0, 1, 4, 9, 100, 121, 144, 169, 400, 441, 484, 676, 900, 961, 1089, 9801, 10000, 10201, 10404, 10609, 12100, 12321, 12544, 12769, 14400, 14641, 14884, 16900, 40000, 40401, 40804, 44100, 44521, 44944, 48400, 48841, 67600, 69696, 90000, 90601

Offset: 1

Author

Amarnath Murthy, May 03 2001

Keywords

• nonn
• base
• easy

Comments

The corresponding square roots are in A102859.

Examples

			169 and 961 are both squares.
1089 = 33^2 and 9801 = 99^2 so 1089 and 9801 belong to the sequence.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
• Index entry for sequences related to reversing digits of squares

Crossrefs

Cf. A102859 (square roots), A033294 (exclude final digit 0).

Programs

Magma

[n^2: n in [0..306] | IsSquare(Seqint(Reverse(Intseq(n^2))))]; // Bruno Berselli, Apr 30 2011

Mathematica

Select[Range[0,400]^2,IntegerQ[Sqrt[IntegerReverse[#]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 29 2019 *)

PARI

{ for(m=0, 1000, my(r=fromdigits(Vecrev(digits(m^2)))); if(issquare(r), print1(m^2, ", ") )) } \\ Harry J. Smith, Jul 23 2009

Python

from itertools import count, islice
from sympy import integer_nthroot
def A061457_gen(): # generator of terms
    return filter(lambda n:integer_nthroot(int(str(n)[::-1]),2)[1], (n**2 for n in count(0)))
A061457_list = list(islice(A061457_gen(),30)) # Chai Wah Wu, Nov 18 2022

Formula

a(n) = A102859(n)^2.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 17 2001