OFFSET
0,1
COMMENTS
Differences of Beatty sequence for square root of 5.
Let S(0) = 2; obtain S(k) from S(k-1) by applying 2 -> 2223, 3 -> 22223; sequence is S(0), S(1), S(2), ...
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = floor((n+1)*sqrt(5)) - floor(n*sqrt(5)).
MATHEMATICA
Flatten[ Table[ Nest[ Flatten[ # /. {2 -> {2, 2, 2, 3}, 3 -> {2, 2, 2, 2, 3}}] &, {2}, n], {n, 0, 4}]] (* Robert G. Wilson v, May 07 2005 *)
Differences[Table[Floor[n Sqrt[5]], {n, 0, 110}]] (* Harvey P. Dale, May 05 2019 *)
PROG
(PARI) a(n)=floor((n+1)*sqrt(5))-floor(n*sqrt(5))
(Magma)
A081147:= func< n | Floor((n+1)*Sqrt(5)) - Floor(n*Sqrt(5)) >;
[A081147(n): n in [0..120]]; // G. C. Greubel, Jan 15 2024
(SageMath)
def A081147(n): return floor((n+1)*sqrt(5)) - floor(n*sqrt(5))
[A081147(n) for n in range(121)] # G. C. Greubel, Jan 15 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 16 2003
STATUS
approved