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

1,1

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001116, A002486, A022844, A120702.

Sequence in context: A119720 A173978 A000134 * A350235 A189752 A206813

Adjacent sequences: A120698 A120699 A120700 * A120702 A120703 A120704

Keyword

easy,nonn

Author

Martin Fuller, Jun 28 2006

Status

approved