OFFSET
0,2
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).
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
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved
