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A004643
Powers of 2 written in base 4.
17
1, 2, 10, 20, 100, 200, 1000, 2000, 10000, 20000, 100000, 200000, 1000000, 2000000, 10000000, 20000000, 100000000, 200000000, 1000000000, 2000000000, 10000000000, 20000000000, 100000000000, 200000000000, 1000000000000, 2000000000000, 10000000000000, 20000000000000
OFFSET
0,2
COMMENTS
Also seems to be numbers k such that the digits of k^3 are cubes. - Colin Barker, Apr 21 2017
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
E.g.f.: cosh(sqrt(10)*x) + sqrt(2/5)*sinh(sqrt(10)*x). - Stefano Spezia, Nov 20 2025
From Amiram Eldar, Nov 21 2025: (Start)
Sum_{n>=0} 1/a(n) = 5/3.
Sum_{n>=0} (-1)^n/a(n) = 5/9. (End)
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 *)
PROG
(PARI) for(n=0, 30, print1(fromdigits(digits(2^n, 4)), ", ")) \\ G. C. Greubel, Sep 10 2018
(Magma) [Seqint(Intseq(2^n, 4)): n in [0..30]]; // G. C. Greubel, Sep 10 2018
(Python)
def A004643(n): return 10**(n>>1)<<1 if n&1 else 10**(n>>1) # Chai Wah Wu, Nov 19 2025
CROSSREFS
Cf. A000079, A000866, A004645, ..., A004655: powers of 2 written in base 10, 4, 5, ..., 16.
Sequence in context: A324474 A294493 A261660 * A284213 A156818 A037422
KEYWORD
nonn,base,easy
STATUS
approved