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

1,2

Comments

Those resulting in leading zeros are excluded.

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Square Number

Example

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

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 *)

Prog

(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

Crossrefs

Subsequence of A000290.

Cf. A045878, A035131.

Sequence in context: A128524 A027451 A227744 * A378492 A354078 A061267

Adjacent sequences: A035124 A035125 A035126 * A035128 A035129 A035130

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 1998

Status

approved