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A081147 Differences of Beatty sequence for square root of 5. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

Table of n, a(n) for n=0..104.

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))

CROSSREFS

Cf. A022839.

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

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)