A046231 Numbers whose cube is palindromic in base 4.

0, 1, 5, 17, 65, 257, 1025, 4097, 16385, 65537, 262145, 1048577, 4194305, 16777217, 67108865, 268435457, 1073741825, 4294967297

Offset

1,3

Comments

No number less than 10^8 has a cube that is palindromic in base 2 or base 3.

Next term exceeds 10000000000. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006

Links

Table of n, a(n) for n=1..18.

Patrick De Geest, World!Of Numbers

Formula

It seems that for n>=2, a(n)=4^(n-1)+1. - Benoit Cloitre, Dec 07 2003

Mathematica

For[i = 1, i < 1000000, i++, tmp = IntegerDigits[i^3, 4]; If[tmp == Reverse[tmp], Print[i]] ]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006 *)

Prog

(PARI) isok(k) = my(d=digits(k^3, 4)); Vecrev(d) == d; \\ Michel Marcus, Aug 02 2022
(Python)
from itertools import count, islice
from sympy.ntheory import is_palindromic as ispal
def agen(startk=0): yield from (k for k in count(startk) if ispal(k**3, 4))
print(list(islice(agen(), 12))) # Michael S. Branicky, Aug 02 2022

Crossrefs

Cf. A046232.

Cf. A052539. - R. J. Mathar, Oct 13 2008

Sequence in context: A273535 A149672 A149673 * A092896 A149674 A149675

Adjacent sequences: A046228 A046229 A046230 * A046232 A046233 A046234

Keyword

nonn,more,base

Author

Patrick De Geest, May 15 1998

Extensions

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006, corrected Nov 01 2006

Status

approved