A035126 -id:A035126 - 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

A353054 Numbers k such that placing the last digit first gives 2k+1.

Original entry on oeis.org

1052, 26315, 15789473, 3157894736, 421052631578, 2105263157894, 36842105263157, 1052631578947368421052, 26315789473684210526315, 15789473684210526315789473, 3157894736842105263157894736, 421052631578947368421052631578, 2105263157894736842105263157894, 36842105263157894736842105263157

Offset: 1

Tanya Khovanova, Apr 20 2022

The digits of all terms appear to be a substring of the digits 105263157894736842 (= A092697(2)) repeated. - Chai Wah Wu, Apr 23 2022

			2*1052 + 1 = 2105. Thus, 1052 is in this sequence.

Chai Wah Wu, Table of n, a(n) for n = 1..389

Other "rotate right" sequences: A035126, A035130.

Subsequence of A034180.

Select[Range[100000000], FromDigits[Prepend[Drop[IntegerDigits[#], -1], Last[IntegerDigits[#]]]] == 2 # + 1 &]

f(n) = if (n < 10, n, my(d=digits(n)); fromdigits(concat(d[#d], Vec(d, #d-1))));
isok(m) = f(m) == 2*m+1; \\ Michel Marcus, Apr 21 2022

from itertools import count, islice
def A353054_gen(): # generator of terms
    for l in count(1):
        a, b = 10**l-2, 10**(l-1)-2
        for m in range(1,10):
            q, r = divmod(m*a-1,19)
            if r == 0 and b <= q - 2 <= a:
                yield 10*q+m
A353054_list = list(islice(A353054_gen(),20)) # Chai Wah Wu, Apr 23 2022

a(4)-a(7) from Amiram Eldar, Apr 22 2022

a(8)-a(14) from Chai Wah Wu, Apr 23 2022

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A035130 Cubes when digits rotated right once remain cubic.

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

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A353054 Numbers k such that placing the last digit first gives 2k+1.

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