A035126 Squares when digits rotated right once remain square.

1, 4, 9, 256, 441, 961, 16641, 48841, 61009, 66564, 1127844, 2537649, 3857296, 4932841, 182682256, 298840369, 342842256, 392872041, 493772841, 787588096, 877996161, 10766967696, 33255899044, 49382172841, 74825772849

Offset

1,2

Comments

Those resulting in leading zeros excluded.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1838

Eric Weisstein's World of Mathematics, Square Number

Formula

a(n) = A045877(n)^2. - R. J. Mathar, Jan 25 2017

Example

2221^2 = 4932841 -> 1493284 = 1222^2. Note that the root behaves accordingly!

Mathematica

Select[Range[300000]^2, IntegerQ[Sqrt[FromDigits[RotateRight[ IntegerDigits[ #]]]]]&] (* Harvey P. Dale, Mar 22 2015 *)

Prog

(Magma) [k:k in [m^2:m in [1..10^6]]| IsSquare(Seqint( (Intseq(Floor(k/10)) cat  [ Intseq(k)[1]])))]; // Marius A. Burtea, Oct 08 2019
(Python)
from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
def A035126_gen(): # generator of terms
    for l in count(0):
        l1, l2 = 10**(l+1), 10**l
        yield from sorted(set(x**2 for z in (diop_DN(10, m*(1-l1)) for m in range(10)) for x, y in z if l1 >= x**2 >= l2))
A035126_list = list(islice(A035126_gen(), 30)) # Chai Wah Wu, Apr 23 2022

Crossrefs

Cf. A045877, A035130.

Sequence in context: A377665 A167657 A175700 * A178454 A051671 A109103

Adjacent sequences: A035123 A035124 A035125 * A035127 A035128 A035129

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 1998

Status

approved