A081168 - OEIS

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A081168

Differences of Beatty sequence for square root of 10.

3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

Let S(0) = 3; obtain S(k) from S(k-1) by applying the morphism 3 -> 333334, 4 -> 3333334; sequence is S(0), S(1), S(2), ...

More generally, for a(n,m) = floor((n+1)*sqrt(m^2+ 1)) - floor(n*sqrt(m^2+1)) start with m and apply the morphism: m -> m^(2m-1), m+1; m+1 -> m^(2m), m+1.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = floor((n+1)*sqrt(10)) - floor(n*sqrt(10)).

MATHEMATICA

Differences[Floor[Sqrt[10]*Range[0, 120]]] (* G. C. Greubel, Jan 15 2024 *)

PROG

(PARI) a(n)=floor((n+1)*sqrt(10))-floor(n*sqrt(10))

(Magma)

A081168:= func< n | Floor((n+1)*Sqrt(10)) - Floor(n*Sqrt(10)) >;

[A081168(n): n in [0..120]]; // G. C. Greubel, Jan 15 2024

(SageMath)