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

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• more
• base

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

• Patrick De Geest, World!Of Numbers, Palindromic cubes in bases 2 to 17.

Crossrefs

Cf. A046232.

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

Programs

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 *)

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

Formula

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

Extensions

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