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
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
KEYWORD
nonn,easy
AUTHOR
Karl V. Keller, Jr., Dec 15 2014
STATUS
approved