A045878 Numbers k such that rotating digits of k^2 left once still yields a square.

1, 2, 3, 12, 14, 25, 108, 122, 216, 310, 1222, 2028, 2527, 3042, 11802, 12222, 13704, 24865, 25185, 26053, 30494, 122222, 208148, 247137, 312222, 1125786, 1222222, 1325080, 2084388, 2551071, 3025794, 3037736, 3126582, 10716846, 10787208

Offset

1,2

Comments

Squares resulting in leading zeros are excluded.

A090843 is a subsequence. - Chai Wah Wu, Apr 23 2022

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Square Number

Example

11303148^2 = {1}27761154709904 -> 277611547099041{1} = 16661679^2.

Mathematica

rlsQ[n_]:=Module[{idnrl=RotateLeft[IntegerDigits[n^2]]}, First[idnrl]>0 && IntegerQ[Sqrt[FromDigits[idnrl]]]]; Select[Range[11000000], rlsQ] (* Harvey P. Dale, Nov 03 2013 *)

Prog

(Python)
from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
def A045878_gen(): # generator of terms
    for l in count(0):
        l1, l2 = 10**(l+1), 10**l
        yield from sorted(set(abs(y) for z in (diop_DN(10, m*(1-l1)) for m in range(10)) for x, y in z if l1 >= x**2 >= l2))
A045878_list = list(islice(A045878_gen(), 30)) # Chai Wah Wu, Apr 23 2022

Crossrefs

Cf. A000290, A045877, A035129, A090843.

Sequence in context: A291565 A299545 A068603 * A295398 A138321 A015756

Adjacent sequences: A045875 A045876 A045877 * A045879 A045880 A045881

Keyword

nonn,base

Author

Erich Friedman

Extensions

More terms from Patrick De Geest, Nov 15 1998

Status

approved