A004643 Powers of 2 written in base 4.

1, 2, 10, 20, 100, 200, 1000, 2000, 10000, 20000, 100000, 200000, 1000000, 2000000, 10000000, 20000000, 100000000, 200000000, 1000000000, 2000000000, 10000000000, 20000000000, 100000000000, 200000000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

Also seems to be numbers k such that the digits of k^3 are cubes. - Colin Barker, Apr 21 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,10).

Programs

Magma

[Seqint(Intseq(2^n, 4)): n in [0..30]]; // G. C. Greubel, Sep 10 2018

Mathematica

Table[FromDigits[IntegerDigits[2^n, 4]], {n, 0, 40}] (* Vincenzo Librandi, Jun 07 2013 *)
Table[{1,2}10^n,{n,0,20}]//Flatten (* Harvey P. Dale, Feb 14 2018 *)

PARI

for(n=0,30, print1(fromdigits(digits(2^n, 4)), ", ")) \\ G. C. Greubel, Sep 10 2018

Formula

From Chai Wah Wu, Sep 03 2020: (Start)

a(n) = 10*a(n-2) for n > 1.

G.f.: (-2*x - 1)/(10*x^2 - 1). (End)

a(n) = (3-(-1)^n)/2 * 10^floor(n/2). - Bernard Schott, Sep 17 2020