A045877 Rotating digits of a(n)^2 right once still yields a square.

1, 2, 3, 16, 21, 31, 129, 221, 247, 258, 1062, 1593, 1964, 2221, 13516, 17287, 18516, 19821, 22221, 28064, 29631, 103764, 182362, 222221, 273543, 1246713, 1509437, 1635219, 1856538, 2222221, 2253804, 2749249, 2784807, 11619096, 11949507

Offset

1,2

Comments

Squares resulting in leading zeros excluded.

(2*10^k-11)/9 are terms, i.e. A165402 is a subsequence. - Chai Wah Wu, Apr 23 2022

Links

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

Eric Weisstein's World of Mathematics, Square Number

Example

13516^2 = 18268225{6} -> {6}18268225 = 24865^2.

Prog

(Python)
from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
def A045877_gen(): # generator of terms
    for l in count(0):
        l1, l2 = 10**(l+1), 10**l
        yield from sorted(set(abs(x) for z in (diop_DN(10, m*(1-l1)) for m in range(10)) for x, y in z if l1 >= x**2 >= l2))
A045877_list = list(islice(A045877_gen(), 30)) # Chai Wah Wu, Apr 23 2022

Crossrefs

Cf. A000290, A045878, A035126, A035128, A165402.

Sequence in context: A122656 A171458 A044905 * A261840 A100643 A067037

Adjacent sequences: A045874 A045875 A045876 * A045878 A045879 A045880

Keyword

nonn,base

Author

Erich Friedman

Extensions

More terms from Patrick De Geest, Nov 15 1998

Status

approved