A035127 Squares which when digits are rotated left once remain square.

1, 4, 9, 144, 196, 625, 11664, 14884, 46656, 96100, 1493284, 4112784, 6385729, 9253764, 139287204, 149377284, 187799616, 618268225, 634284225, 678758809, 929884036, 14938217284, 43325589904, 61076696769, 97482577284

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Comments

Those resulting in leading zeros are excluded.

Examples

			2527^2 = 6385729 -> 3857296 = 1964^2.
		

Links

• Eric Weisstein's World of Mathematics, Square Number

Crossrefs

Subsequence of A000290.

Cf. A045878, A035131.

Programs

Mathematica

okQ[n_]:=Module[{idn=IntegerDigits[n]},idn[[2]]!=0&&IntegerQ[Sqrt[ FromDigits[RotateLeft[idn]]]]]; Join[{1,4,9},Select[Range[4,320000]^2, okQ]] (* Harvey P. Dale, Apr 30 2011 *)

Python

from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
def A035127_gen(): # generator of terms
    for l in count(0):
        l1, l2 = 10**(l+1), 10**l
        yield from sorted(set(y**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))
A035127_list = list(islice(A035127_gen(),20)) # Chai Wah Wu, Apr 23 2022