A120701 Number of unit circles which fit touching a circle of radius n-1, i.e., with their centers on a circle of radius n.

2, 6, 9, 12, 15, 18, 21, 25, 28, 31, 34, 37, 40, 43, 47, 50, 53, 56, 59, 62, 65, 69, 72, 75, 78, 81, 84, 87, 91, 94, 97, 100, 103, 106, 109, 113, 116, 119, 122, 125, 128, 131, 135, 138, 141, 144, 147, 150, 153, 157, 160, 163, 166, 169, 172, 175, 179, 182, 185, 188

Offset: 1

Author

Martin Fuller, Jun 28 2006

Keywords

• easy
• nonn

Comments

Coincides with A022844 = floor(n*Pi) except at n=1, 25510582, ... (sequence A120702).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001116, A002486, A022844, A120702.

Programs

Magma

R:= RealField(30); [Floor(Pi(R)/Arcsin(1/n)) : n in [1..70]]; // G. C. Greubel, Aug 25 2023

Mathematica

Table[Floor[Pi/ArcSin[1/n]], {n, 60}] (* Indranil Ghosh, Jul 21 2017 *)

Python

from mpmath import mp, pi, asin
mp.dps=100
def a(n): return int(floor(pi/asin(1./n)))
print([a(n) for n in range(1, 61)]) # Indranil Ghosh, Jul 21 2017

SageMath

[floor(pi/arcsin(1/n)) for n in range(1,71)] # G. C. Greubel, Aug 25 2023

Formula

a(n) = floor(Pi/arcsin(1/n)).