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

Author

Benoit Cloitre, Apr 16 2003

Keywords

• nonn

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

Crossrefs

Cf. A022839, A081168.

Programs

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

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 *)

PARI

a(n)=floor((n+1)*sqrt(5))-floor(n*sqrt(5))

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

Formula

a(n) = floor((n+1)*sqrt(5)) - floor(n*sqrt(5)).