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

Offset: 1

Author

Karl V. Keller, Jr., Dec 15 2014

Keywords

• nonn
• easy

Examples

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

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

Crossrefs

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

Cf. A253301 (complement).

Programs

Mathematica

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

PARI

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

Python

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

Formula

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