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
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
Programs
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Mathematica
a252169[n_] := Floor[#*Sqrt[Pi*((1 + Sqrt[5])/2)]] & /@ Range@n; a252169[58] (* Michael De Vlieger, Dec 27 2014 *)
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PARI
vector(100,n,floor(n*sqrt(Pi*(1+sqrt(5))/2))) \\ Derek Orr, Dec 30 2014
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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)).