A035128 -id:A035128 - cp's OEIS frontend

A035130 Cubes when digits rotated right once remain cubic.

1, 8, 125, 54439939

Offset: 1

Patrick De Geest, Nov 15 1998

Those resulting in leading zeros excluded.

			5^3 = 125 -> 512 = 8^3.

Eric Weisstein's World of Mathematics, Cubic Number

Cf. A035126, A035128, A035131.

[k^3:k in [1..100000]| IsPower(Seqint((Intseq(Floor(k^3/10)) cat [Intseq(k^3)[1]])),3)]; // Marius A. Burtea, Oct 08 2019

Select[Range[10000]^3,IntegerQ[Surd[FromDigits[RotateRight[ IntegerDigits[#]]], 3]]&] (* Harvey P. Dale, May 25 2015 *)

a(n) = A035128(n)^3. - R. J. Mathar, Jan 25 2017

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

Original entry on oeis.org

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

Erich Friedman

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

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

Chai Wah Wu, Table of n, a(n) for n = 1..1838
Eric Weisstein's World of Mathematics, Square Number

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

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

More terms from Patrick De Geest, Nov 15 1998

A035129 Rotating digits of a(n)^3 left once still yields a cube.

Original entry on oeis.org

1, 2, 8, 457

Offset: 1

Patrick De Geest, Nov 15 1998

Cubes resulting in leading zeros excluded.

			457^3 = 95443993 -> 54439939 = 379^3.

Eric Weisstein's World of Mathematics, Cubic Number

Cf. A045878, A035128.

cp's OEIS Frontend

A035130 Cubes when digits rotated right once remain cubic.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Extensions

A035129 Rotating digits of a(n)^3 left once still yields a cube.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs