A252169 - OEIS

A252169

Beatty sequence for sqrt(Pi*phi) where phi is the golden ratio A001622.

2, 4, 6, 9, 11, 13, 15, 18, 20, 22, 24, 27, 29, 31, 33, 36, 38, 40, 42, 45, 47, 49, 51, 54, 56, 58, 60, 63, 65, 67, 69, 72, 74, 76, 78, 81, 83, 85, 87, 90, 92, 94, 96, 99, 101, 103, 105, 108, 110, 112, 114, 117, 119, 121, 124, 126, 128, 130

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

OFFSET

1,1

LINKS

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Beatty Sequence.

Eric Weisstein's World of Mathematics, Golden Ratio

Eric Weisstein's World of Mathematics, Pi

Index entries for sequences related to Beatty sequences

FORMULA

a(n) = floor(n*sqrt(Pi*phi)) = floor(n*sqrt(Pi*(1+sqrt(5))/2)).

EXAMPLE

For n = 5, floor(5*sqrt(Pi*(1+sqrt(5))/2)) = 11.

MATHEMATICA

a252169[n_] := Floor[#*Sqrt[Pi*((1 + Sqrt[5])/2)]] & /@ Range@n; a252169[58] (* Michael De Vlieger, Dec 27 2014 *)

PROG

(Python) from sympy import *

for n in range(1, 3001): print(floor(n*sqrt(pi*(1+sqrt(5))/2)), end=', ')

(PARI) vector(100, n, floor(n*sqrt(Pi*(1+sqrt(5))/2))) \\ Derek Orr, Dec 30 2014

CROSSREFS

Cf. A000796 (Pi), A001622 (golden ratio, phi), A094886 (Pi*phi).

Cf. A253301 (complement).

Sequence in context: A248898 A207188 A085148 * A187842 A330000 A059566

Adjacent sequences: A252166 A252167 A252168 * A252170 A252171 A252172

KEYWORD

nonn,easy

AUTHOR

Karl V. Keller, Jr., Dec 15 2014

STATUS

approved