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

1,3

Comments

The corresponding square roots are in A102859.

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

Formula

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

Example

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

Mathematica

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

Prog

(PARI) { n=0; for (m=0, 1110100, x=m^2; r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); if (issquare(r), write("b061457.txt", n++, " ", m^2)) ) } \\ Harry J. Smith, Jul 23 2009
(Magma) [n^2: n in [0..306] | IsSquare(Seqint(Reverse(Intseq(n^2))))]; // Bruno Berselli, Apr 30 2011
(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

Crossrefs

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

Sequence in context: A245241 A115690 A115689 * A069707 A129967 A182020

Adjacent sequences: A061454 A061455 A061456 * A061458 A061459 A061460

Keyword

nonn,base,easy

Author

Amarnath Murthy, May 03 2001

Extensions

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

Status

approved