A081147 First differences of A022839.

2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2

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

Cf. A022839, A081168.

Sequence in context: A187186 A259651 A253719 * A236103 A278293 A163671

Adjacent sequences: A081144 A081145 A081146 * A081148 A081149 A081150

Keyword

nonn

Author

Benoit Cloitre, Apr 16 2003

Status

approved